If you’re looking for a good Star Trek game, the best modern one is the New Horizons mod for Stellaris. The mod is an entire game by itself and is absolutely worth the price of admission imo.

Star Trek Online is a solid MMORPG that provides an engaging experience for fans of the Star Trek franchise. While the game has its flaws, such as dated graphics, lackluster ground combat, and some pay-to-win elements, its space combat, character customization, and vast universe more than make up for these shortcomings.

Try it out. There is a lot of story content to explore for a new-comer, they try to basically pick up any thread from canon that wasn't resolved, and spin a new story from it. It's very much a fan service / theme park style of game. They even got several Star Trek alumni to provide their voice to the game.

Yes, a F2P game is worth trying. If you like Star Trek it is good fun. Keep in mind the game doesn't do a good job of explaining some aspects of the way it works. For example, there's no instruction on how to get more abilities for your bridge officers, or how to competently setup the weapons and consoles on a ship.

No. It is very likely to remain active for many more years because the Star Trek franchise has been quite active in recent years and looks to be continuing on from there.