There's a bit of a thing behind this, I think. My guess is you don't so much need answers to your actual questions as you need some kind of criteria to base your own decisions during play yeah?
So, the stuff on your sheet that you get straight at chargen is kind of special, right? To the point where you're specifically told to lay off it a little bit as MC - you can target the Gunlugger with bad moves, but him losing his guns is a serious deal you don't spring unless he really, really asks for it.
Stuff gained at chargen as well as stuff gained through advancement has a bit of plot armour - in the first case, it's not the first thing the MC targets, in the second, it's something that you can get by 'skipping' the detailed fiction of actually doing it and thus skipping all of the things that could have possibly gone wrong (so if you remove "Avoiding a Dude" as an Operator, the dude maybe just stops paying attention to you and you don't talk much about it).
Stuff I gain through the fiction has no such mild plot protection. If I'm a Driver and I have a at-chargen car, the car is unproblematically mine (with just a sprinkle of problems to keep it interesting) - I have an assumed source of fuel, a dude who does maintenance on it, and a general acceptance of the less-threatening NPCs that the car is mine and that they should stay well away of it.
If I'm a Chopper and I get my gang a bunch of guns off of corpses, it's more problematic - I might not have a source of armour, the things may need serious repair after the battle, and the corpses might have some friends that'll want to have stern words with me. I get the gun upgrade alright, but I also get a problem.
Now, this is somewhat more controverstial, but a case can be made that some kind of plot protection extends to negative "stuff" you get at chargen, too. For example - if the Hardholder gets rid of an Obligation want by shooting the dude he was obliged to, he certainly gets rid of it. But, if you still want to play and have the hardholder's Wealth move still have an interesting miss result, you can just think up a different Want to sub in for the one that got picked at chargen.
So, while you treat the fiction seriously - what happens changes stuff around your sheet, as well, your job as MC is to pay a certain amount of special respect to the stuff your players got through chargen or advancement, and none to the stuff they get through play.
The balance is a bit like making custom moves. You don't make a free Sharp based custom violence move, but you still allow the -1 Hard Driver to go aggro. You don't give a Brainer a grenade launcher to buy at a town market, but he can certainly try to mindfuck a compound tough out of one.