Asalamu Alykum Mia
Whats important to note is that a "sin" is something and "disbelieving" is another thing.
A person is not in a state of disbelief if he/she had not rejected the truth.
The verse below is speaking to the people receiving the message of the Quran and telling them do not setup rivals while you know the truth of the matter. Before you may not of known but now you have been brought the truth.
(2:22) Who has made the earth your couch, and the heavens your canopy; and sent down rain from the heavens; and brought forth therewith fruits for your sustenance; then set not up rivals unto Allah when ye know (the truth)
The word "kaffaru" means disbelieved after truth has been made clear and known. If a person chooses to live his/her life as a disbeliever and die in that state of disbelief, God is telling us on the Day when we are called for Judgment, God will not forgive such a person.
From the following verse, I find that if a person has believed and accepted the truth, and then goes to let go of the truth(believing and worshipping God, and thinking about the Day of Judgment) and increases in disbelief, God will not accept their repentance. Also the second scenario is that if a person dies in a state of disbelief also God will not forgive them.
3:90-91 Lo! those who disbelieve after their (profession of) belief, and afterward grow violent in disbelief: their repentance will not be accepted. And such are those who are astray. (90) Lo! those who disbelieve, and die in disbelief, the (whole) earth full of gold would not be accepted from such an one if it were offered as a ransom (for his soul). Theirs will be a painful doom and they will have no helpers
And also, for those people who have sins and transgressed against their souls in anyway, whether they setup rivals with God or not, who committed mischief, and think of themselves they are no good, God is telling them don't lose hope, despair not of the Mercy of God. He forgives all sins. Of course these are people who did not know and they did not have a messenger and were not guided before.
39:53 Say: "O my Servants who have transgressed against their souls! Despair not of the Mercy of Allah: for Allah forgives all sins: for He is Oft-Forgiving, Most Merciful.
Again for people who believe and the message has been manifested and they know the truth, God warns them do not associate or make partners with God or worship anything other than God. He may forgive all sins even as a believer but "associating partners and worshipping other than God" they will not be forgiven. So a believer might make mistakes, might fall in sin throughout his/her life and make bad judgment and calls, but his belief is solely in God and relies on Him and asks for forgiveness and prays and repeatedly tries not to sin. He knows there will be answering for his ways on the Day of Judgment.
(4:115-116)And whoso opposeth the messenger after the guidance (of Allah) hath been manifested unto him, and followeth other than the believer's way, We appoint for him that unto which he himself hath turned, and expose him unto hell - a hapless journey's end! (115) Lo! Allah pardoneth not that partners should be ascribed unto Him. He pardoneth all save that to whom He will. Whoso ascribeth partners unto Allah hath wandered far astray.
you asked: "Also, does Allah forgive disbelief if you repent?"
I would say Despair not in the Mercy of God. If a person denied the truth somehow some way and he/she is shown the right away again from the Mercy of the Lord, and repents, believes, and righteousness then possibly yes. If they die in a state of disbelieve, God says that people which truth has been manifested to them and clearly shown the way and continue to deny God then no. On the Day of Judgment they will not be forgiven. That is the ultimate test at the end. These are the guidelines and rules set by God.
Peace