1. I think
Em,
Emmy, and occasionally
Emma are the most likely nicknames. I doubt anyone would use
Emily as a nickname, but I can easily imagine a stressed or careless reader glancing at the name and reading it as
Emily.
2. Yes, all the time.
3. I think
Emilia and
Emma are quite different from
Amy.
Emmy is much closer.
4. Yes, they're very sweet for sisters!