I've only read one series that uses them.. as far as I can remember? There might be a few more, but this one I'll mention was the only one that popped up in my mind.
It's a monthly-ish comic that started half a year ago and I'm really digging it for the boxing it's got. Looks super promising!
I find the animated panels in it pretty cool. Just one panel for each episode, very smooth and minimal for the most part. There's so few comic artists out there who make attempts at animating, so like, I'll take what I can get if I come across it. I appreciate the effort to add something a little extra to a comic, especially animation since lord knows that's a lot of effort to put into a few seconds.
To answer your questions..
I think it adds to the story, but it also takes away from it kinda. Some might prefer the motion to be presented in a still image, and from that standpoint, I'd kiiinda agree? BASH is a bit of an exception as I feel like the motion would've been drawn exactly the same, so it's not too big a deal there. The artist clearly knows how to present it both ways. But for other comics though, maybe they wouldn't have the same feel in that aspect. So.. the effort could be put towards creating more chapters or using the animation as promotional material rather than using small bits for a panel. Not that I don't appreciate it, but just.. there's better places to use it?
For the best way to use them.. motions that are tough to communicate through a still image alone would be the best use obviously, but outside of that? Subtle animations would be cool to see if you wanna move away from characters talking for a bit. Like fire in the background or smoke from a cigarette actually moving, maybe grass or hair flowing in the wind, lights flickering ever so slightly.
And as for the best way to make them.. I'm not gonna act like I know how to animate so I can't give a take on programs or advice on compressing or none of that. However.. I can vouch for repeatable loops. I typically don't like seeing the obvious ending of a scene in gifs in general, so that's a bit of a bias on my end, but I do think it has more.. replayability that way. Also, smooth loops are just satisifying to watch so there's that.