Antinomianism states that your actions cannot matter as long as you believe rightly.

2 Timothy 2:25 in humility correcting those who are in opposition, if God perhaps will grant them repentance, so that they may know the truth,

Repentance is no more of a work than is believing. To ignore repentance is to ignore the very reason we believe rightly. Without repentance you do not believe rightly. You only believe in a license to sin and have purchased fire insurance.

Are we saved by grace alone? Undoubtedly.
Acts 11:18

When they heard these things they became silent; and they glorified God, saying, “Then God has also granted to the Gentiles repentance to life.”

2 Corinthians 7:10

For godly sorrow produces repentance leading to salvation, not to be regretted; but the sorrow of the world produces death.

James 2:19

You believe that there is one God. Good! Even the demons believe that--and shudder.

Those that believe repentance is a state of sinless perfection are those that do not believe rightly and look for justification of their sins.

Romans 6:1-2

“What shall we say, then? Shall we go on sinning so that grace may increase? By no means! We died to sin; how can we live in it any longer?”

Summary of my belief: You cannot be saved without God's grace through God granted faith in Jesus Christ alone; but you cannot have true faith without God granted repentance.

-Repent and believe and you will be damned to hell for eternity
-Believe without repentance and you will be damned to hell

One of the main points of difference that exist within the Lutheran doctrine of the solas is simply that Luther's belief is that after man's fall into sin, he completely lost his ability to choose freely to be obedient. So freewill doesn't exist in a man's fallen state in order to respond with, and because of the bondage of his will he rather is completely dependant upon God's grace alone through faith in what Christ did alone for salvation. As well this ties directly into God satisfying His own desire of whom He himself has pre elected or predestined to be heirs of salvation. Martin Luther referred to a believer as "snow covered cow dung" as part of his forensic justification teaching, where Christ's alien righteousness covers the sinner before the eyes of the Father. This is a short explanation of the psychology behind the support for the teaching of faith alone.

On the other hand true faith is determined differently by other believers in the context whereby God's judgement towards our deeds bears witness for the existence of faith. That being simply put we are actively setting aside our will freely for His will. Though it's true we do have a tendency toward sin by our fallen nature and have need of a redeemer, we have a choice to respond to His light, and are accountable for that response to Him as for whether we have welcomed it, and have abided or not abided in it. Jesus informed that there were "people who honor me with their lips, but their hearts are far from me". This clearly demonstrates a man's ability to be genuine in his response to God's calling or the knock at the door of his heart. It's an understanding that supports genuine inner change through the graceful presence of Christ's own Spirit making an impact directly within our hearts. Its regenerating affect on man convinces of God's will as having the better interest for his life, and a difference in attitude is what truly defines faith as described by Jesus when He said "you must be born again". This is what's revealed from our fruits when considered as a child of God, or one who does the will of the Father who the Son names on judgement day as His brother, sister, mother etc. This kind of believer is actively sealed by the Spirit and graced with the justifying backing of Christ's own blood, and the follower is in communion with God and does not shun His presence. As well it's understood in general that though the Spirit pursues in a mysterious manner, its also believed God desires all men to be saved and come to the knowledge of the truth. For its written that every act of His kindness towards us is a chance to repent. 😇 God bless!

Faith works together with repentance

You cannot separate repentance from salvation-faith. Put simply, faith that leads to salvation works with repentance.

The Bible clearly teaches that repentance is necessary for salvation and it works by faith (Matthew 3:2; 4:17; Mark 6:12; Luke 5:32; 13:3; 24:47; Acts 2:38; 11:18; 17:30).

Repentance involves a complete change in the mind and will of the believer. It is more than mere sorrow for sin; it is a complete turning from sin to God in faith. This is how Wikipedia captures it:

"Repentance is a theological term that describes a stage in Christian salvation where the believer turns away from sin. As a distinct stage in the ordo salutis its position is disputed, with some theological traditions arguing it occurs prior to faith and the Reformed theological tradition arguing it occurs after faith.[1] In Roman Catholic theology repentance is part of the larger theological concept of penance.[2] Generally in the Old Testament the term repentance comes from the Hebrew word group that means "turn away from."[3]:1007 Sometimes this word group is employed to request a turning from sinful activity (Jeremiah 8:6). In the New Testament theμετανοέω/metanoeo word group can mean remorse but is generally translated as a turning away from sin (Matthew 3:2).[3]:1007 Theologically 'repentance', the turning away from sin is linked to a corresponding turn to faith in God.[3]:1008" https://en.m.wikipedia.org/wiki/Repentance_(Christianity)?_e_pi_=7%2CPAGE_ID10%2C7837090973

Faith takes place when there's a change from taking an action based on reason to just assenting the mind to the truth of what is declared by another, it's a change from unbelief to belief. That change is what is called repentance.

"to open their eyes, and to turn them from darkness to light, and from the power of Satan unto God, that they may receive forgiveness of sins, and inheritance among them which are sanctified by faith that is in me" ( Acts 26:18).

This is a summary of a lecture from my college lecturer Mark Baddeley. Sentences in quotes (but not block quotes) are from his lecture notes.

The relationship of faith and repentance

There are several views of the relationship of faith and repentance. By considering their implications we will see which coalesces with our understanding of the gospel best.

Faith is an aspect of repentance

This can seem like a good position, because we do after all repent from our unbelief as we come to faith. We turn our backs on our life of independence and rebellion against God and lean on him in faith.

But if we think of repentance as we usually do, the changing of our lives from acts of sin to acts of righteousness, and if we think of repentance as the dominant category in salvation, then not only is this a denial of sole fide, but we simply will never be able to do it. None of us in this life fully repent.

Alternatively we can limit our category of repentance to an attitudinal and relational return to God. This doesn't deny sola fide, but neither does it give any basis for the specific acts of repentance. The good works we do in "repentance" are in fact disconnected from the relational repentance that is foundational.

Both options are majorly flawed in that they separate repentance from the gospel and the word of God. We can know the law from nature (Romans 1), so that is the prerequisite for repentance. "If repentance is the big category, and faith is the small one, if repentance is the big story and faith is one chapter within it (part of turning from sin to God is that we turn form unbelief to faith) then repentance must begin and be sustained without any reference to the word of God, let alone the gospel--for that is the office of faith." Which means repentance is moralism and legalism.

Faith and repentance arise together

If we consider repentance to be necessary for justification, then all the problems of the first option still apply.

Or we might say that repentance is not necessary. Perhaps faith is related to justification and repentance to sanctification. But this even further disconnects the gospel from sanctification. Preaching the gospel no longer makes people holy, instead reminding them of the law does. This leads to the kind of view that says that Jesus Christ is our saviour but not our lord. Faith is necessary for salvation, but repentance is only necessary for discipleship.

Faith produces righteousness

Calvin's Institutes, Book 3, Chapter 3:

The sum of the Gospel is, not without good reason, made to consist in repentance and forgiveness of sins; ... Now, since Christ confers upon us, and we obtain by faith, both free reconciliation and newness of life, reason and order require that I should here begin to treat of both. ... That repentance not only always follows faith, but is produced by it, ought to be without controversy. For since pardon and forgiveness are offered by the preaching of the Gospel, in order that the sinner, delivered from the tyranny of Satan, the yoke of sin, and the miserable bondage of iniquity, may pass into the kingdom of God, it is certain that no man can embrace the grace of the Gospel without retaking himself from the errors of his former life into the right path, and making it his whole study to practice repentance. Those who think that repentance precedes faith instead of flowing from, or being produced by it, as the fruit by the tree, have never understood its nature, and are moved to adopt that view on very insufficient grounds.

The key to Calvin's view is that repentance is a blessing of the gospel, not a precondition to receiving the blessings. God gives us both forgiveness of sins and repentance; newness of life is both repentance and sanctification.

"The problem with both 'repentance produces faith' and 'repentance and faith arise together and independently from each' is that this means that liberation from our bondage to sin is no longer a gift of the gospel, no longer an effect of the word of Christ for us. ... The only way that repentance and the gospel can be linked, such that repentance is actually produced by the gospel, is if repentance is (like everything else in salvation) something given by the gospel itself. This is because the only thing that links us to the gospel is faith."

"Once again, faith has no inherent virtue, it is just the conviction of the truth of God’s mercy to us in Christ, it is knowing something. It can’t produce anything by its own power. What faith does is relate us to God and connect us to Christ, in whom everything we need is stored, and so we receive the gift of repentance. It is actually union with Christ that produces repentance, faith is the instrument by which we receive it (and everything else we need for life and salvation)."

Coming back to the OP's questions

Here's how I would answer the questions posed to us by the OP.

1. How does repentance fit into this doctrine?

   If you accept this argument, then repentance cannot be a prerequisite of either faith or salvation. It is a gift we receive alongside the forgiveness of our sins.

2. Is it possible to be unrepentant of sin (whether for some sins or all sins that one has committed) and yet still receive pardon for those sins?

   This is not only possible, it is unavoidable in this life. As long as we live we sin and we are incompletely and insufficiently repentant.

3. Is repentance considered a "work" in that it is ultimately unnecessary for justification?

   Repentance is not so much a work, as the fruit of salvation which then grows more good works. It is not necessary for salvation, but neither is it optional. In the gospel God makes dead people alive, he makes ignorant and disbelieving people into people who know God and trust him. In just the same way he turns unrepentant people into repentant people. It would not make sense for God to leave any living person in a state of unrepentance, and we can ultimately suppress our new repentant nature no more than we could make ourselves alive while we were dead.