Thanks to Intel's marketing prowess, people generally equate clock speed (GHz these days) with performance. Although clock speed and performance can be related, be careful comparing clock speeds especially across a range of chip mfgrs. AMD lost out for a long time because their chips performed better (read: more efficiently - doing more relevant "stuff" per clock cycle) at a lower clock speed. Eventually AMD smartened up and that's why we started seeing chips with names like AMD Athlon 2800 XP (its clock speed was 2.083GHz but performed roughly the same as an Intel 2.8GHz chip).
But to answer your questions!
1.) Best to think of it as affecting in some way just about everything that goes on with your PC.
2.) Your motherboard may support a faster CPU than what you've got, and buying a faster CPU would up your "GHz". You'll have to check your motherboard manual (or google, etc.) to check for sure.
Another way to change "GHz" is to
overclock your system, but I strongly recommend against doing that unless you have much experience with that already.
What are you looking to do with your computer? It may be that a RAM upgrade or video card upgrade may give you the performance gain you're looking for (in the area you care about!).