I agree. I agree because she knows that he just got angry and people do mean stuff when they are angry...

Yes I think so.

No. Not even a little. Calling a person a slur, especially someone you say is your friend, isn't acceptable. Particularly if your only excuse is that you were angry.

Lily made it clear that calling her a mud blood was simply the last straw in a chain of offenses. He would apologize, but then continue doing the same things over and over again (she gave him the choice between her and dark magic and GUESS WHAT HE CHOSE). It just wasn't until then that she admitted to herself that the relationship was toxic and he wasn't someone she wanted to be around.

It's was also Snape that started the hunt for the 'Chosen One' when he told the part about the prophecy to Voldemort, even knowing that it would lead to the death of a baby. Then he only insisted on saving James and Harry because Dumbledore told him she wouldn't leave them to die.

Lily made the smart choice in throwing out that trash and he still managed to get her killed.

If Snape had actually turned away from the dark arts after he apologized to Lily, it could have made sense for her to accept his apology eventually. The way things went, Snape gave her no reason to forgive him. At least, not until after she died.

I think so...yes