I don't understand the "atonement through Christ's death". How does the death of someone, especially if they know they are divine and will rise again, atone for the sins of someone else? Is it like if I pay for someone else's parking ticket?
Kind of, but not really. From Leviticus 17:11: "For the life of the flesh is in the blood, and I have given it for you on the altar to make atonement for your souls, for it is the blood that makes atonement by the life." So God gave a way for people to atone for their sins through blood sacrifice, otherwise all would perish. However, it's not something he desired; the tribes of Israel were using it as a loophole instead of an actual act of contrition (See Isaiah 1:11-17).
That makes sense in terms of financial punishment, but it doens't make sense for person A to spend time in jail for a murder commited by person B.
Sins are sometimes referred to as debts. For instance, in some Bible translations, you'll see the Lord's Prayer as "forgive us our debts as we forgive others' debts" instead of "forgive us our sins, as we forgive those who sin against us." So when you commit a sin, you essentially have a debt that needs to be paid.
Why would God accept payment for that? Surely God knew that Jesus's death was not permanent?
Yes, of course he knew Jesus would be resurrected. That was always a part of the prophecy regarding the Christ. As to why he selected this method to allow all people to atone for their sin, I'm afraid I can't give a complete answer to that, but I'm not sure anyone can. God says in Isaiah 55:8-9 "For my thoughts are not your thoughts, neither are your ways my ways...". From the best of my ability to understand, it has to do with his desire to show mercy to the world, but still uphold justice.