can i do serious rock climbing if i have sweaty hands

That depends if you can cure the problem using chalk. Some people sweat so much that the rock feels greasy regardless of how much chalk they use, and that is a huge disadvantage. Get treatment if you have palmar hyperhidrosis (google this). it is a curable medical condition.

Yes. Everyone has their shortcomings in climbing, and the point is to overcome them. Try cooling off your hands before climbing, by putting them in a deep dark crack or anywere cool. And of course, use chalk. You will find it easier climbing outside - indoor plastic holds and sweaty hands make it really tough, especially in the summer time!

Use chalk. Most climbing shops sell climbing chalk and chalk bags. The chalk will absorb the moisture on your hands and give you a better grip (the same reason that gymnasts use it).

yeah, but you will go through more chalk than most people. there is a product out, l do not remember what it is called or if it is even available without a prescription, but basically it is like a deoderant stick for your palms. it is some kind of anti-perspirant. so if your palms sweat really bad, go talk to a pharmacist and see if they have anything over the counter. otherwise, chalk will most likely do the trick for you.

You get sweaty hands a lot try getting some gloves that grip to the rock.