You likely just scratched the solder mask off. If you have a magnifier it would be a good idea to get in there and see whether or not any of the traces are cut.
It depends on what trace was cut, or even whether one was cut at all. The tiny bit of copper is the trace, since the solder mask (the green stuff) was scraped off it'll be exposed. Is the trace squiggly or much more straight? Does it lead to anywhere in particular like a header on the board? Some of the traces on the bottom are superficial since they lead to unused debugging headers and the like.
Definitely not fun but I'm not certain that's the cause of the error code still present on the box. The scratch appears really light only affecting the solder mask. I believe those traces are the high speed interconnect between the CPU and GPU and not related to power.
No, that isn't normal. If the GPU/ CPU were properly soldered in then you would not have to use the heatsyncs to press the points together.
Heat gun? It would be cheaper to bring send it to Shawnunderse7en or just to a local computer repair shop.