If Satan fell because of sin, then was there sin in heaven at that point? Assuming that God cast Satan out of heaven because of his sinful pride and attempt to dethrone God, then doesn't that mean that there was, at that point in time, some sin in heaven? This seems like it would disprove the statement that there can't be any sin in heaven.

If there can, then, then why can't those dwelling in heaven think sinful things, too? It's said in the Bible that you can't be "unsaved", so then I'm guessing that means that He won't throw anyone out of heaven once they're in. What would he do in the event that someone sinned in heaven?

I asked my pastor this once, and he directed me to a passage in Ezra, I think; unfortunately, I don't remember exactly where...
Sin is not in the atmosphere of a place, but in the person who disobeys God. Places don't disobey God, do they, so heaven itself does not have sin. It appears that you are thinking that sin is spread into the atmosphere like germs, and cause people to start thinking sinful things. 

Sinners can entice others to sin by their actions and words. In Revelation 12, Satan is thrown out of heaven "and his angels," which implies that other angels have either fallen on their own, or were influenced by Satan. 

However, Satan is still under the rule of God and is called back to heaven now and then, as we see in Job 1 and 2. So heaven at times is inhabited by sinning creatures.