There are full auto weapons capable of chambering the .308 Winchester, yes, although these were actually designed for the dimensionally similar (but not identical) 7.62x51 cartridge. M14, AR10, CETME, G3, FN FAL, just to name a few.
Yes, the Glock 18 is fully automatic.
Yes, the M14 is capable of fully automatic fire.
100-500 or so
100-700 usd
No, it is a semi-automatic.
No you have to pull on the trigger every time you want it to fire. But you can easily make it fully automatic.
Fully automatic shotgun, no. Automatic rifles and machine guns, yes.
I know of no place that permits fully automatic firearms to be used in hunting.
No. Spring powered means spring powered. Not fully automatic.
No, just semi automatic.
100-1000 usd
The first fully automatic shotgun was the AA-12