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Freddy vs. Jason showed what happened between Jason Goes to Hell and Jason X.
They are studying Jason's regenerative powers at the Crystal Lake Research Facility, so supposedly he has had enough time to grow back his hair and skin since he was captured.
Again, we assume he has regenerative powers.
The large room in which he was held must have had several exits.
There was a cut scene showing Rowan with a box of Crystal Lake paper clippings and other Jason material, and his machete was one of the items in the box.
Apparently, Jason is just that strong.
It is never fully explained, but we are to presume that after seeing the carnage that Jason left, anybody that would have come to investigate would have decided that it was best to leave him frozen. There was also some mention of the Crystal Lake Research Facility being closed down soon, so it's possible that this was so top secret that the people on the other end didn't know about it yet, so that information died with Dr. Wimmer.
Presumably in the future they made cryogenic chambers that were self-propelled and didn't need an outside electrical source.
He is holding only the back of her head and dunking her face in, and presumably thought the nitrogen was just water in which he could drown her.
Brodski used the jet pack on his spacesuit to escape and fly around to the side.
Very possibly, but odds are this question will never be answered properly, given that we didn't see Jason's final state in this movie (i.e. whether he was disintegrated completely on re-entering Earth II's atmosphere, leaving only his mask, or whether he survived and the mask was simply separated from his head), and the franchise reboot means that there will likely be no future film to fill in the gaps. The script has someone pulling Jason's mask out of the water at the end (though doesn't specify if it is Jason), and comic books show that Jason did survive the end of this movie; whether or not you count them as being a proper part of the Friday the 13th storyline is largely down to personal taste.
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