1. You already have your trophy case visible on your profile, so I assume you're referring to an unofficial trophy someone gave out for a contest they hosted here on the forum. Only official trophies can be seen on the trophy widget. If you want to display unofficial trophies, you could make a custom widget on your profile or add your unofficial trophies somewhere in your About Me.
2. Unofficial trophies are just pixel art. You can make them in a bunch of programs, but I personally use
paint.net.
3. You can either show off a build here in the forum in the appropriate section or post a build you made in the
Maps section of the site. You could also post an image of a build as a wall post, but don't follow that advise to post it as a blog unless you're going to write about the build in some capacity (what your idea was when you built it, a review of another person's build, etc.). Blogs aren't just an image repository.
4. To make a collection, go to any submission on the site (map, skin, etc.) and click the Collections drown-down on the right. You can click the plus button there to make a new collection.