The computer thing has been confusing me. I could have sworn that the first time I tried to use a computer while in PA, I got a message stating that I couldn't do that. Since then, I've been reading terminals and hacking without getting out of my PA, and I haven't had that problem again.
In Fallout 3, all the (humanoid) NPC companions could wear PA with no training, so that limitation seems to only have ever applied to the Lone Wanderer.
I always remove my power core to be safe. Settlers will only grab the armour during an attack, but raiders can also take it. I learned that the hard way in the Corvega factory. I got out of my armour to try and find a way up to the office area (didn't see the button to extend the walkway at first). While I was up there, a few more raiders wandered in, and one of them stole my T45! That was also when I learned that if someone dies in PA, you can't take back the frame.