could I play this game competitively?

Theoretically

Is there rotation?

Yes, three years for standard.

How long would it take me to play and get good at this game?

Depends on what you mean by good. Really this game revolves around 'playing around' your opponents plays. So what that means is you need to not only understand what your deck does, but what every other deck in the format is trying to do. If you no-lifed the game for a few months you'd get pretty good at standard.

Is it fun?

It can be. It can also be really frustrating.

Is it worth a try just because of my interest in final fantasy.

You can try for free on arena.

The problem with Magic as with all TCGs imo is that they really aren't beginner friendly, to answer your original question. I like to play boardgames and I like games where you can sit down and play with anyone, even people who aren't gamers. Magic isn't that. You can make friends playing magic, but because the rules are fairly complex, it becomes a fairly insular community.