1. When you raise a glass of wine or champagne, or any other kind of alcoholic drink, to 'toast' someone, i.e. to honor them or congratulate them on something, one often says 'here's to you'. It means 'we are raising our glasses (of wine, champagne, etc.) to you to show you that we are congratulating you or honoring you.' In other words, it is a traditional saying.
2. No, you would not say 'here's for you' because it would simply be incorrect. You could, though, say: 'Here, this is for you' if you were giving someone something, but it would not be the correct usage when toasting someone.
3. Yes, you have the correct meaning for 'backed them up'.
4. Informal English can sometimes be rather ambiguous. 'Hell' is a usually word with negative meanings, but here it is used to mean 'a lot'. (I miss you a lot.) The irony here is that the writer has probably just realized the irony of that ambiguity, i.e. no one would miss hell, but at the same time, the writer is in a kind of personal 'hell'.