In response to your questions:
1. Yes. If it's a separate assembly, then it won't matter if it's in c#
2. I'd say yes - it will help to keep your MVC stuff separate, but of course you will need the basic bootstrap stuff in your base webforms project. Good idea.
I've recently started with MVC into an webforms site, and it's well worth the effort.
also view stakeflow for more info.