does it use the processor or does it use the graphics card for this?
Either or both. GPUs that support CUDA (Nvidia) or OpenCL (AMD) will complete the work units magnitudes faster than even high-end CPUs, so using those is preferable when possible.
how does this help biological questions?
The research is on proteins, which assemble themselves by "folding" their chains in order to do their work of breaking down food, regulating mood, combating disease etc. If this folding malfunctions there can be serious effects on health, so the aim of the research is to better understand the processes involved. To properly do so requires modeling the huge number of possible folding permutations that can occur, which is done by mathematical modeling. This is where folding@home comes in....
how many problems do they have?
A lot! Certainly many millions.
what is the thing that is really going on during the process? From point a (Stanford) to point b (computer) point c (Stanford)?
Perhaps these links will answer some of your questions better than My own limited understanding will allow:
About the science of Folding@home
Folding@Home - Wikipedia