Okay, so as usual I feel the need to explain away plot holes (I do it myself naturally during any film if the film warrants it, ie. when they aren't gaping from a script written in crayon
They vary well may have done. Jaylah had traps and jumped in to fight Kralls goons without a second notice so I assume that she was a fly in the ointment they just stayed away from after any contact. If she wasn't doing any harm why waste time and resources on her. She wasn't a threat in their eyes, unless attacked, like an animal.
I believe the cloaking was more about protection from those drones chasing Bones and Spock.
Jaylah had most of the work done before Scotty brought Starfleet Academy training and ingenuity to the table. We needed more technobabble to show this which is a big flaw in the script for me.
I think this was already explained by @KandorLives
He's Captain Kirk. You answered your own question.
As anyone with chronic SAD will attest, we already have artificial sunlamps. 300 years down the line I imagine they'll be much more efficient, closer to the real thing and regularly used by the federation in space.
Well, that's the point really, a Starbase is there as a pit stop in space for Starfleet vessels so the closer to unexplored territory the better as your fleet then has a further range. I imagine civilians were there as they were either connected to Star Fleet personnel, passing through at a federation stop off point or providing a service of some sort (think Quark or Garak on DS9).
That I can't help with. Why they thought it was good is beyond me. This should have been called into Darkness, the title would have suited it better. Into Darkness should have been called Star Trek: The Flaccid Resentment Of Khan, but then they thought lying to us to try and make Khan a surprise was a good idea. Mind you, that was only the third or fourth worst idea they had making that film.