Well normal power supplies are built to the ATX form factor, making them compatible with ATX cases. Sometimes OEMs like HP or Dell use smaller, uncommon form factors. You'll have to find out if the case for this computer fits an ATX power supply.
Why do you want to upgrade? Are you upgrading the graphics card?
Ah, thats going to be a pretty beastly gaming rig once your done with it! ;-)
I think I would just recommend you get a new case, unless you are buying a 670 with a blower type fan. We dont even know if the 670 will fit in the case.
Well 'normal' atx cases use 120mm or 140mm fans, but I'm not sure if that case uses those sizes, it probably uses one 120mm exhaust fan and some weird 83mm intake. The temps wont be dangerous, they just wont be good. Are you getting a blower type 670?