If my lymph nodes are "clear", do I still need chemotherapy?

Maybe. Chemotherapy is recommended after breast cancer surgery based upon the probability of cancer cells being elsewhere in the body. Having clear lymph nodes certainly reduces this probability, but cancer can still spread through the bloodstream or alternate routes outside of the armpit. Therefore, we also look at the size of the cancer and specific patient and tumor factors before deciding.
Depends. Nodal status is important, however it is not the only thing that determines the stage and the need for certain treatment like chemotherapy. It will also depend on the type of cancer, the size of cancer, biology of the cancer/ prognostic factors.Etc. Discuss in detail with your oncologist.