I just picked up a cheap classical second hand. It seems to be really old. I think it's an Ariana. Anyway, there's a small crack in the side of the headstock and there's a quarter sized gash in the top of the guitar (the part that faces the ceiling when I play). It doesn't go all the way through, but I think if I pushed it it would.

I like the way the guitar plays and sounds and was debating whether or not to have a luthier fix these problems. Is it even possible?
possible but not worth it. go to projectguitar.com and do it yourself
Guessing the top gash would cost you in the region of £80 to £100 to get fixed so agree with the above that its prob not worth getting someone else to do.