What are the rules for copy write and corporate trademarks such as Star Trek ™?

I heard about the confiscation of “unauthorized merchandise” sales at conventions. These were products made by the fans and then on sale at the convention. Why did they get into trouble? Was it related to their use of the Property Star Trek, and would they have been safe had they generically labeled the product something else like “replica of scanning device.” instead of “replica of star trek VI tricorder”?
I would like a complete answer, or as complete as possible.

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