Answer 1:
As far as we know, the fastest possible speed is the speed of light. It is impossible for any kind of matter to move at the speed of light. We can get closer and closer, like 99.9999% of the speed of light, but that requires exponentially more energy to do so.

Answer 3:
There is none  molecules can move arbitrarily fast. Actually, there is a limit  the speed of light  but as a molecule (or anything, for that matter) approaches the speed of light, it becomes infinitely energetic. The E = 1/2 m v^{2} rule doesn't work close to the speed of light (or it does, but m goes to infinity). Because temperature refers to the energy of the molecule and not the speed, temperature itself can still theoretically be infinite.
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