Yes, exactly that. You don't have to earn points for posts likes, set the points earned to zero and users will still receive a badge but no points towards their level.
I allow users to earn points for most things. For example, 100 posts and no likes would be level 3, 50 posts and 50 likes would be level 6. I encourage higher quality posts this way.
No, I meant point count. If I understood you correctly, you wanted to give users points for reaching X amount of points which is not possible.
Displaying "featured badges" is a built-in option, and badges can be automatically featured. I've yet to try it, but I think it features the latest badge you earn.
And yes, it's the forum in my signature.