I'm responding from the point of view of programming rather than art, so I don't know if this'll be useful. That said:
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I’ve never heard of sprite sheet animations done in 60 fps, so I did quite a bit of research on the net, which states some games use variable frame rates, with sprite sheets running at a lower frame rate than the game itself.
1. Just wanted to check if this holds true for most games, or if I misunderstood something?
I think that's probably true, generally speaking. Different games handle timing differently, but frame rates for sprite animation can certainly be independent of the game's frame rate (and probably usually are, I'd imagine). Also, I'd guess sprite animation frame rates are probably often less than the game frame rate.
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2. Is 12 fps not used to animate sprite sheets in 2D mobile platform games?
I don't think there's anything particular special about platform games here, or maybe even about mobile games. That said, 12 FPS certainly seems reasonable for certain art styles. Maybe artists can weigh in on that part.
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The programmer in the team sent feedback that the sprite sheet was not smooth, and should be meant to run in 30 fps (mobile) or 60 fps (PC).
It might be worth asking for some clarification on this. 'The sprite sheet was not smooth' is a bit ambiguous (that could, for example, mean that the graphics are too pixelated), but based on the rest of the discussion I assume they're talking about smoothness of animation.
With respect to that, for me at least it's not immediately clear what 'meant to run at 30 or 60 FPS' means. If you haven't already, maybe you could just ask the developers what they want the frame rate of the animation to be (that is, how many frames per second), and what its duration should be.
Again, I'm answering as a programmer. Maybe some artists can give you a better answer.