What will Snape do now that he's no longer in love with Lilly?

Nothing. They are no longer counting on him to protect Harry from a returned Voldemort. Unless you mean whether he is going to evolve as a person and maybe develop a love life.

How was magical Italy ruined 323 years ago, or does it matter?

I suspect it was only an example of how yes, Potterverse magic can be that destructive (something we would not guess based on canon).

Quirrell teaching students the Killing curse...will it matter?

Unlikely. Knowing the Killing Curse is perfectly legal, and a lot of people have managed to learn it even though it is not taught in school. Come to that, the information we have suggests that it is also perfectly legal to use, just not against humans (unless they are Death Eaters, assuming the Monroe Act hasn't been repealed).

Why did the rememberal go off?

Because Harry has a lifetime's worth of lost/repressed Tom Riddle memories. We know that they're still in there somewhere, because he recovers the memory of his imprinting and of the locations of Voldemort's five "elemental" horcruxes.