To the Calvinist, what does it mean that in the beginning God already has His object of wrath?

Firstly, the use of "And what if" at the start of the sentence is a rhetorical device. It is not asking a question, thus making Paul unsure as to whether this is or is not the case. Rather, it follows on from his other rhetorical questions, e.g. "But who are you, O man, to answer back to God?"

John Calvin addresses this in his commentary on Romans (emphasis mine):

A second answer, by which he briefly shows, that though the counsel of God is in fact incomprehensible, yet his unblamable justice shines forth no less in the perdition of the reprobate than in the salvation of the elect. He does not indeed give a reason for divine election, so as to assign a cause why this man is chosen and that man rejected; for it was not meet that the things contained in the secret counsel of God should be subjected to the judgment of men; and, besides, this mystery is inexplicable. He therefore keeps us from curiously examining those things which exceed human comprehension. He yet shows, that as far as God’s predestination manifests itself, it appears perfectly just.

The particles, εἰ δὲ, used by Paul, I take to mean, And what if? so that the whole sentence is a question; and thus the sense will be more evident: and there is here an ellipsis, when we are to consider this as being understood, — “Who then can charge him with unrighteousness, or arraign him?” for here appears nothing but the most perfect course of justice.

Secondly, the objects of His wrath do not become the objects of His wrath AFTER their creation, because it says He prepares them. Taking into account also the context of Jacob and Esau being loved/hated before their birth, it is not a case of them being born, doing deeds, and then becoming objects of wrath. They are objects of wrath prepared for destruction from before their birth.

In Calvin's commentary on Romans, he also says the following:

But if we wish fully to understand Paul, almost every word must be examined. 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.

From this we can understand that God does intend from the beginning to destroy those He has elected to be vessels of wrath, but He doesn't destroy them immediately. Rather, His wrath is deferred until the Day of Judgment.

Thirdly, your second question asks "Does God wants His objects of wrath to repent or not?" While this could be perhaps more thoroughly addressed, essentially He does not intend for His objects of wrath to ever repent. There is a general sense in which His will is for all men to repent, but His effective will is clear here; there are those chosen who will never repent, because God creates them such that they will never repent. We know that the gospel is for all men from various parts of the Bible, but we also know from various parts of the Bible that God has chosen those who will be saved and those who will not be saved.