1. You can use any core theme to base a new one on.
Base is a real bare-bones theme with basic layout only, no colors etc. It's a better basis for creative themes where you plan a lot of changes and don't want to be overriding styles all the time (as people used to have to do in 1.9). It's not really designed to be usable as a theme itself. And yes we should be correcting obvious layout problems in Base.
Standard (which is itself based on Base!) is a smoother usable theme for development purposes, more like the standard that everyone is used to from Moodle 1.x. It's still fairly minimalist. It's going to be a good basis for simpler themes that just want to add a few colours and images.
2. Yes, plugins should take care of their own Base layout in their own styles.css (example for forum)