Did John Calvin teach that God creates certain souls only to be destroyed?

Calvin is correct in his written understanding of what the Bible teaches. God created the vast, overwhelming majority of humans to suffer in this life and for eternity, because it pleased him. Which is precisely why I no longer accept the Bible as THE word(s) of God. The internal contradictions on the nature and personality of God with the conclusion of double-predestination is good only for those who "believe".

Your quote describing predestinarianism is clearly referring to a certain interpretation of Romans 9. Romans 9, after all, uses similar verbiage:

You will say to me then, “Why [then] does he still find fault? For who can oppose his will?” But who indeed are you, a human being, to talk back to God? Will what is made say to its maker, “Why have you created me so?” Or does not the potter have a right over the clay, to make out of the same lump one vessel for a noble purpose and another for an ignoble one? What if God, wishing to show his wrath and make known his power, has endured with much patience the vessels of wrath made for destruction? This was to make known the riches of his glory to the vessels of mercy, which he has prepared previously for glory, namely, us whom he has called, not only from the Jews but also from the Gentiles.

Here's what John Calvin says about the passage:

The reason why what is formed ought not to contend with its former, is, that the former does nothing but what he has a right to do. By the word power, he means not that the maker has strength to do according to his will, but that this privilege rightly and justly belongs to him. For he intends not to claim for God any arbitrary power but what ought to be justly ascribed to him.

And further, bear this in mind, — that as the potter takes away nothing from the clay, whatever form he may give it; so God takes away nothing from man, in whatever condition he may create him. Only this is to be remembered, that God is deprived of a portion of his honor, except such an authority over men be conceded to him as to constitute him the arbitrator of life and death.

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He then argues thus, — There are vessels prepared for destruction, that is, given up and appointed to destruction: they are also vessels of wrath, that is, made and formed for this end, that they may be examples of God’s vengeance and displeasure. If the Lord bears patiently for a time with these, not destroying them at the first moment, but deferring the judgment prepared for them, and this in order to set forth the decisions of his severity, that others may be terrified by so dreadful examples, and also to make known his power, to exhibit which he makes them in various ways to serve; and, further, that the amplitude of his mercy towards the elect may hence be more fully known and more brightly shine forth; — what is there worthy of being reprehended in this dispensation? But that he is silent as to the reason, why they are vessels appointed to destruction, is no matter of wonder. He indeed takes it as granted, according to what has been already said, that the reason is hid in the secret and inexplorable counsel of God; whose justice it behoves us rather to adore than to scrutinize.

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Though in the second clause he asserts more expressly that it is God who prepares the elect for glory, as he had simply said before that the reprobate are vessels prepared for destruction; there is yet no doubt but that the preparation of both is connected with the secret counsel of God. Paul might have otherwise said, that the reprobate give up or cast themselves into destruction; but he intimates here, that before they are born they are destined to their lot.

So in essence, yes, Calvin believed in an eternal decree to save some sinners and leave others to the destruction that their sin deserves.

To answer the second half of the question, Calvin believed that a Christian can have assurance of salvation, but warned that there are wrong ways to achieve such assurance. The first, as he writes in Instruction in Faith, is to look to the decree itself:

Let us take from the lot of both the elect and the others, reasons for extolling his glory. On the other hand, let us not seek (as many do), in order to confirm the certainty of our salvation, to penetrate the very interior of heaven and to investigate what God from his eternity has decided to do with us. That can only worry us with a miserable distress and perturbation. Let us be content, then, with the testimony by which he has sufficiently and amply confirmed to us this certainty.

Another wrong way is to look chiefly to oneself, as he describes in his Institutes of the Christian Religion (book 3, chapter 13, paragraph 13):

Let the most perfect man descend into his own conscience, and bring his actions to account, and what will the result be? Will he feel calm and quiescent, as if all matters were well arranged between himself and God; or will he not rather be stung with dire torment, when he sees that the ground of condemnation is within him if he be estimated by his works? Conscience, when it beholds God, must either have sure peace with his justice, or be beset by the terrors of hell. We gain nothing, therefore, by discoursing of righteousness, unless we hold it to be a righteousness stable enough to support our souls before the tribunal of God. When the soul is able to appear intrepidly in the presence of God, and receive his sentence without dismay, then only let us know that we have found a righteousness that is not fictitious.

Calvin writes in a number of places that "the certainty of faith depends on the grace of Christ alone," and that, "We must begin with what is revealed in Christ concerning the love of the Father for us and what Christ Himself daily preaches to us through the Gospel." In other words, for assurance of faith we look to 1) the perfect obedience of Christ, 2) the mercy of God, and 3) the promises of salvation God gives to his church based on the first two items.

But in his commentary on 1 John 3:14, he says:

For as no one sincerely loves his brethren, except he is regenerated by the Spirit of God, he hence rightly concludes that the Spirit of God, who is life, dwells in all who love the brethren. But it would be preposterous for any one to infer hence, that life is obtained by love, since love is in order of time posterior to it.

The argument would be more plausible, were it said that love makes us more certain of life: then confidence as to salvation would recumb on works. But the answer to this is obvious; for though faith is confirmed by all the graces of God as aids, yet it ceases not to have its foundation in the mercy of God only. As for instance, when we enjoy the light, we are certain that the sun shines; if the sun shines on the place in which we are, we have a clearer view of it; but yet when the visible rays do not come to us, we are satisfied that the sun diffuses its brightness for our benefit. So when faith is founded on Christ, some things may happen to assist it, still it rests on Christ’s grace alone.

One way of reading this is that, to have confidence that we stand on the promises of God, we look chiefly to the strength of the foundation (Christ), but we can also to some degree look at whether we have built on that foundation via good works ("love of the brethren" chief among those works).

So to sum up: a person can have assurance that they themselves are elect by looking firstly unto Christ and his promises, then to one's works which are a fruit of saving faith. Assurance is not found by excessive introspection or by inquiring into the decree of election itself.

While I believe Calvin can accurately be stated to have "systematized" Calvinism, it received more systemization and scrutiny over the course of the following centuries. But, remarkably, the confessions of the reformed churches reached the same conclusions regarding assurance as he did.

_{All scriptural citations are from the NABRE. Though I prefer the Battles translation of the Institutes, I don't know where it can be found online so I quoted Beverige for ease of cross-reference. I am much indebted to the article Calvin's Doctrine of the Assurance of Faith by David B. McWilliams for a lot of the content of this answer.}

More or less, yes, but the question is slightly misleading by the word 'only' (but about that later). As this discussion is so complex and visited by so many people with so many quotations, etc., I prefer to try and give you a summary view from many years studying many books on the subject. Mine is not the 'only view' but really on this question you can only get a well-read opinion.

Calvin, like St. Augustine before him believed in dual predestination, whereby God determines in advance of one's birth, if they will ultimately perish or be saved. However unlike St. Augustine who did not believe that we could obtain clear assurance that we are 'the elect' the reformation largely developed by Luther and then in some sense 'systematized' by Calvin, as you say, added the belief that one could and should enjoy the confidence of knowing they are 'elect'.

The doctrine is more or less just a simple resignation to some bible verses that seem to say exactly the same thing. For example if one just accepts these words without much resistance they automatically become a Calvinist of some sort:

For the Scripture says to Pharaoh, “ For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth.” So then he has mercy on whomever he wills, and he hardens whomever he wills. You will say to me then, “ Why does he still find fault? For who can resist his will?” But who are you, O man, to answer back to God? Will what is molded say to its molder, “ Why have you made me like this?” Has the potter no right over the clay, to make out of the same lump one vessel for honorable use and another for dishonorable use? What if God, desiring to show his wrath and to make known his power, has endured with much patience vessels of wrath prepared for destruction, in order to make known the riches of his glory for vessels of mercy, which he has prepared beforehand for glory — even us whom he has called, not from the Jews only but also from the Gentiles? (Romans 9:17-24, ESV)

Now it is difficult to accept this doctrine for two reasons, one good and one bad. The good reason is that we say but 'What about God's love?' and the bad reason is just human pride that will not accept being liable to destruction on any account but 'demands' God's love, even when fully deserving eternal wrath.

Now we come to the word 'alone'. This is the hinge where controversy turns, because it either allows God to be full of love for sinners, or refuses it. If we were to say, 'Did God only created the Devil and the apostates in hell, for the 'sole purpose' of simply suffering, in order that God might be glorified' we would be going a tad further than what anyone has ever believed as we would absolutely be excluding his love for sinners in every way. We would not allow any other reason (.i.e., some loving reason) for their being created other then their destruction (which seems like hate to me). If we say that 'God created the Devil and apostates in hell, full knowing that they would only end up in hell, although they may have served another purpose, yet, nevertheless as they will be in hell, it is now there ultimate purpose for being created as respects there own life', we would be more along the lines of a Luther or Calvin.

But back to the question about God's love. Here is where Calvin does seems to fail somewhat, compared to say Luther. Luther would say, yes God chooses without men's will determining anything, yet he would also say God loves each one and to resolve the contradiction he would say, I do not know, it is a mystery, both are true and the answer is hidden from puny men. Calvin would not directly disagree with Luther but he simply would leave some of the encouragements about God's general love for all, absent from the discussion, leaving some with the impression that his view of God was a cruel one. In this sense yes, as great as he was in explaining so many doctrines possibly better than any other before him since the Apostle Paul himself I think he makes the impression that his hear was starting to grow a little cold on this subject as he did not seem to make much effort countering the balance of election and God's boundless love. In other words, I am a Calvinist and although I do not disagree with anything Calvin said on the subject of election, I do disagree on what he left out of the subject, which other like Luther put almost front and center.

Now regards assurance, this is quite straightforward. The Calvinist belief is that anyone who sincerely believes in Christ, and has at least some moral assurance from a changed life aft conversions and a sense of their adoption by the Holy Spirit, proven foremost by their love of other believers, can and do entering into a blessed assurance of their eternal blessed state. I guess we could say this is the warmer side to Calvin, for although he has little heart to consider God's love for the damned, he swings the gates wide open for the enjoyment of God's love without fear for any who flee from God's wrath to the dying love of Christ.

While generations before Calvin and Luther had to suffer without any assurance of their good state, performing penances and various works that were not able to cleanse the conscience, believers now filled with assurance really had the impetus to break away from every kind of cold legalism. If you read Christian history, what really happened after Calvin was an explosion of missionary work across the globe as had never been seen before. This was partly due to the discovery of the new world and exploration of Europeans, but at the same time knowing God's love without fear, must have made people have a bit more heart for the lost and the opportunity of finding eternal security. Therefore although the doctrine seems to have a cold edge to it, it many ways it seems to produce a warm effect and confidence in the free love and grace of God. Seems almost like a contradiction, yet, so does the love of God and his dealings with Pharaoh. Maybe Luther had it right. Don't try and explain it just believe both. God loves everyone and he elects some to heaven and some to hell according to his unknowable judgments and omniscience.

Note: ( I apologize that I do not have the time to collect a bunch of quotations to prove my summary but I actually have already posted them all in other answers on the same subject, so If asked about a particular point I might add a link to another answer where requested.)