1) Typically find them online from webstores. There's lots, do your own homework for finding them. Some specialty parts you may only be able to find from obscure websites or you'll have to fly to Japan and look at random hobby shops who just so happen to have some random part.
2) Personally I'd just bypass the fuse and straight wire it. If you don't want to do that just get a bigger fuse? If you're holding down the trigger for long periods of time and that's what's making it blow you're letting the fuse heat up and blow which is what's causing it.
You can also use a nail or copious amounts of tin foil as a stand in for a fuse:
3) AEG = Automatic Electric Gun. Basically uses electricity form a battery to automatically spin gears and pull back the piston (as opposed to spring power/springer where you're manually cocking the gun after each shot or gas powered (GBB = Gas Blow Back, NBB = Non Block Back (typically gas powered, but does not give recoil)) where it releases gas and due to gas expansion propels the BB).