1. Yes you can use plugins with ClassiPress, but we can't give you a guarantee each and every one of them ever made will be compatable with it, much like any other WordPress theme in that regard really.
2. Yes, there is a custom forms and fields feature built into ClassiPress which allows you to customize the ad form that your customers see, and this include creating multiple custom forms specific to categories.
3. You can allow your users to add Youtube embedded clips such as what you see
here in the ClassiPress demo.