It depends more on the case - the thing is extremely long and wide. And with an I7-6800, the 4080 makes no sense, because you immediately hit a CPU limit, which slows the card down. But it fits on the mainboard and the power supply can cope with it...

It will fit without any problems, the power supply is sufficient for it, only your CPU could slow down the card under certain circumstances. But you can still install it.

I don't think so, because the mainboard is too old and the power supply is not powerful enough for a 4080.

I would try a 30th series, maybe a 3060 ti or 3070.
With those you should get a better result with the setup.

A big performance difference is rarely noticeable.