Yes. A gauge transformation isn't a coordinate transformation.So I guess gauge invariance is another issue.
No, I'm not sure because the only gauge theory I've studied is QED, and it was a long time ago. Now that you mention it, gravitons have spin 2. Not sure what that means though. There are a few threads here where the question of whether gravity is a gauge theory is debated. I think the conclusion was that it's not a gauge theory in the traditional sense, but the answer still depends on what exactly you mean by a gauge theory. I still think that what I said is correct, but if someone tells you that I'm not and they sound like they know what they're talking about, they're probably right.Are you sure spin 0 and spin 2 can't be properties of gauge invariance but only spin 1/2? How come?
I think it can be treated as a potential in approximate calculations, but as I said, it was a long time ago.Btw.. in QED.. do they analyze the electric field as coulomb potential or only as virtual particles... like every analysis in QED involves perturbation of particles?