Yes, exactly. And trademark (and patent) law is different form copyright law in that you MUST defend against any and all infringement, or you risk losing in court and have your trademark/patent be voided.
This. In order to maintain their trademark which they self evidently would want to, the owner must object to unlicensed uses, or the word will get to the point where it is considered generic, and will lose protection. Escalator, linoleum, yo-yo, kerosene, even heroin, all once trademarked and now considered generic terms in the US, in many cases because the owners were cavalier in protecting them. It's this reason that Coca Cola get cross about people using their trademark 'Coke' with a small 'c' as a generic term. They would haughtily point out that Coke is a protected name for a cola flavoured soft drink. Starfleet, and even Starfleet Academy, are registered trademarks so must be defended. Especially where someone else is making money from your trademark.
In the early 00s there was a rush of fan websites getting C&D letters about the use of fonts which had been created as copies of those used in show marketing - WB properties in particular like
Buffy. We got a lot of "won't someone think of the children?!?!" then too, but it's the same dilemma - the protection of IP, especially of a going concern (
Buffy still is even now, thanks to comics) is necessary. It's fine to talk about the show, review it, obsess over it, gather to celebrate it, but once you start using trademarks to do so, or copyrighted IP, or start making it appear that your actions are sanctioned or licensed, you are going to have lawyers knocking.
The Federation? Hah... There have been so many "federations", so absolutely out of CBS reach.
As a generic word, yes, probably not trademarked. But use it in creative works (such as leaflets, posters, videos) in a context that makes people associate it with the "Federation" seen in official Star Trek productions and you certainly wouldn't be outside CBS' grasp. Copyright is broader in that context than trademark.