As far as I'm aware fighters are just big drones that can warp...
So the logical answer would be that Assuming your fighters attack the rats you will both get the bounties/security increase.... However I am certainly far from convinced that this would be the case.
Reason I say this is, you have given agro by your fighters firing at the target, no doubts about this, you would not be able to jump due to timers etc. However, in my experience you usually only receive bounties if you are on grid, you clearly won't be, so it depends which mechanic is considered primary in this case. I would suspect it would be the fire mechanics and that you will indeed receive bounties, but you would need to ask a carrier pilot to know for sure!
Unfortunately for point 2, I'm not familiary with the GCC acronym, but I could take a stab and say as a general rule, anything the ship that has the fighters assigned does will effect both players just like drones. Security hit, agro mechanics including timers everything... Thats why you only assign drones/fighters to players you trust.
Only other thing to note with fighters, you have to launch them while outside your pos, they can be ordered to protect someone or assist someone then I believe you may retreat inside, but you have to be clear of the shield to launch them for sure.
You cannot cloak while you have fighters out... This leads to a bad day when your fighters shut down and become detached, you then have to hope the system is quiet, get warp in's from fellow pilots and scope them to drone bay... it's not pretty!
Lastly, as far as I'm aware (and I'm not certain on this one) fighters can not use acceleration gates!