Dose basal cell cancer increase my risk for melanoma?

A little bit. Yes, but not a great deal. The good news is that surveillance for any skin cancer is the same. Examine your own skin regularly, and keep your scheduled appointments with your doctor or dermatologist. Notify them if you see any lesions which are concerning for skin cancer. Best wishes!
Sightly. Both are related to sun exposure. However because you have had a basal cell carcinoma the incidence of melanoma is small. You should be screened regulary for new skin cancers of all types.
Yes. Having one type skin cancer does raise your risk of developing the others. It is important to wear sunscreen and to limit your exposure to uv radiation. In addition you should see your friendly dermatologist on a regular basis for complete skin examinations.