Is 310 - 320FPS ok? my sites limit for fully auto is 350FPS so my thinking is that this is a bit low It's fine. I'ts not that 30 fps will get you shot.
Will my LiPo batteries kill my gun? Are they too powerful? I have heard horror stories of LiPos stripping gearboxes apart Yes. 11.1 lipo is a bit too much. 7.4 would have been enough.
Should i upgrade the gearbox? If so what gear set would you recommend? No.
Should i shim the gears? They are okay.
Should i get a MOSFET? If so what brand or model With that lipo you probably should.
The piston and spring assembly, should i change those? Also how do I make the seal better? No. How do you know it's not good now?
I the G&G stock motor decent? or should i upgrade this too? It's fine.
Should i change the barrel to a tighter one or leave it as it is? You souldn't.
Should i change the hop up or even go for an R-hop? No and oh god, no.
Should i changed the battery connectors from Tamiya to Deans? So far i don't see an issue with the Tamiya ones. Yes. Tamiya is made for much less currents. Deans (or XT60) have much bigger contacts. If the tamiya gets warm after some quick shots, you should definiately change it.
Any other upgrades you can think of that will improve its performance?
As you can read, my opinion is that you should use the gun and play a lot of airsoft. Currently the gun is not the weak point. Usually beginners think they get shot because others have better guns. An experienced player has the knowledge to get you, it doesn't matter what gun you have. Stock G&G is fine. If it's your only gun you probably shouldn't try to fix it (it's not broken) there is a very real chance it won't be better or even it will be worse.
Sorry, it sounds a bit harsh, it's just my advice based on my experience.