My favorite explanation for ships caps is that you have a certain number of pilot "memories" stored and you produce clones for those memories to inhabit. When you produce a new ship you also create an instance of that pilot/crew to fly it, however do to the psychological stress of the process it is deemed "unsafe" (ominous!) so it only allows one instance of each pilot at a time. The caps are where they are at because of finite storage for these memories (keeping in mind many ships have more than 1 crew member) and the best determinable combination of pilots was stored for humanity's final push. This also explains your special ship selection at the beginning of each game, those pilots were set aside as a wildcard to help improve your odds.
Since all AI ships are, well, AI controlled when you capture a research station or advanced factory you gain the appropriate knowledge to be able to remote control a small portion of those ships without needed a crew. Or maybe remote control pilots residing on your home station, after patching into a small bit of the AI network (assisted by the capture of fabricator, ARS and advanced factories).
I have no idea about turret caps, though. Maybe their targeting systems require some terrabytes of memory and every turret is only equipped with a pentium II or something?
Clearly all the processing for the turret fire control is done by your home station and it only has so much available processing power to deal with the appropriate turret caps. Other command stations that you build just work as a relay to the whole system, which is why your caps don't go up as you build more command stations. This is also why you lose only if you lose your home station, all of the pilot memories and processing power comes from there, so you've got nothing you can do aside from hope for the best of your fleets thats now abandoned in the middle of space.