How many lymph nodes are affected with melanoma?

Hopefully none. If caught early enough, no nodes will be involved, and excision of the cancer site will be curative. Sentinal lymph node biopsy can be helpful to determine if a more extensive lymph node removal needs to be considered. Seek out an established melanoma treatment center or at least a surgeon well versed in melanoma treatment.
It depends. Melanomas have the potential to spread throughout the body via the lymphatic system. For this reason, a sentinel lymph node biopsy is performed for staging any melanoma > 1mm thickness. If the sentinel lymph node contains cancer and there is no gross evidence of metastatic disease, more lymph nodes are removed to provide better local/regional control and potentially prevent more distant spread.
Depends... Advanced melanomas are thought to be spread primarily through the lymphatics. Thus, as a part of staging, if the melanoma is deep, it is generally recommended for one to undergo sentinel lymph node biopsy to capture the 1st few nodes that the melanoma site is drained into. This is only for the purposes of staging and not treatment. If positive, it indicates that the tumor has spread.