I was wondering whether you should use a local script or a regular script when playing an animation in a player's character
Can other players see the animation if filtering enabled is on, and the animation is played on a local script?
Yes. Because the character's Humanoid replicates to the server, playing animations locally will replicated to the server automatically. A rule of thumb is to do whatever you can on the client, as to not slow down the server. And because you can do this on the client, you should.
If you were going to play animations for NPCs that everyone would see, you could do this on the server. But in this case, play the animations locally and they'll replicate.
I am almost 100% sure that animations can only be played from local scripts. As for the FE thing I have no clue sorry. My guess would be that FE doesn't impact the animation even if in a local script