Is this even possible?
I never have seen anything like that. Normally you render a frame as fast as possible do some CPU frame post- or pre-processing and render the next one, so usage flaps between 0 and 100%. Only rarely the FPS are limited to a maximum number and only in this case would this be a meaningful number.
I think it's impossible, cos GPU consists of many parts and each of them could be a bottleneck.
You can test for these bottlenecks though, to see where you need to optimize.
Nope. It's even hard to rigorously define in such a highly parallel environment. However you can approximate it with ARB_timer_query extension.
Not really, but you can get differente performance counters using your vendor's utilities, for NVIDIA you have NVPerfKit and NVPerfHUD. Other vendors have similar utilities.