Pretty much what Sojourner said. Hell, I've created faux book covers, movie posters, etc, using images from actual eps, and have never even given a second thought to using them. I'm not selling them, so I don't worry about it. That and given the massive amount of others doing the same, the odds of anyone in a position to do anything to me actually seeing my stuff and singling me out are astronomical.
When you say "Command Badge" do you mean the arrowhead design used by the Enterprise crew? Or do you mean the Command division badge, as opposed to the Sciences division badge, or the Operations division badge? Or even "Comm badge" even though they didn't have those in ST as they used communicators?
There's too much "badge" in this post.