It'll almost certainly (not actually tested since 3.3, but that's how it worked before) go away after it's over. On the bright side, it's a lot easier in 3.3 to maintain an Investment state for an extended time, and to restart it once it does end.
Changes of controlling faction at a station won't give you *more* stuff in total, but if it's to a different government type will give different stuff. So you may get some benefit if you can make sure each station is controlled by a different government type. Of course, that's then several factions to maintain in Investment rather than just one, and you may need to do a lot of shuffling of factions around to test which government type gives the most modules of types you want at each station.
It requires patience, but if you submit a CG for a new station in the system (poke around the Community Goals subforum for some explanatory threads and the form), you may be able to get some better outfitting as a result. You'll probably only be able to do that once, and it might take years to get to the front of the queue, so don't expect quick results from that. This is also the only real way at the moment you can get a population increase, and it probably won't be a major one.