Yes, that’s what I’m referring to. And a least as far as I remember, it does. It’s not obvious and not addressed at all, but instantaneous travel between two points in space (if you don’t take a shorcut through an addtional dimension, e.g. something we could call w if the three space dimension we’re familiar with are x,y,z) is equivalent to time travel. The same is true for FTL travel, which Star Trek solves by warping space time, which also works.
Perhaps the mycelial network is basically an extra space-time dimension, but at least the way I remember it being explained that wasn’t really the case.
But that’s anyway a relatively technical points and Star Trek, as much as I love it, was never really about the technical things.
Yes, it does. By blowing over it, you evaporate some of its water, which cools it down. See also https://en.wikipedia.org/wiki/Enthalpy_of_vaporization