Hi, welcome and thanks for taking interest in Vivvo
1. I have just installed Facebook connect plugin on demo.myvivvo.com, and it works without any issues, so you can go and take a look on how it works
2. Unfortunately no, current version only works with 3.0.x versions of IPBoard.
3. Yes, it's possible to have different templates for different categories.
You can read more on categories here
4. No, only for entire website.
5. Yes. Every Vivvo license comes with mobile template set by default.
You can read more on Vivvo and how it works on our online documentation