Yes, you can message others on ebay, you just can't get their email address unless you complete a transaction with them.

Yes, I have received some nasty ones. They usually go something like this:

"Thanks for outbidding me at the last possible second, you expletive expletive. You're the biggest expletive expletive on ebay. Expletive expletive expletive. Go expletive yourself and die."