Am I at a higher risk for melanoma due to basal cell skin cancer?

Yes. Basal cell carcinoma is one o the most common malignancy in the us. Risk factors include uv radiation from sun exposure. This also increases your risk of melanoma. Make sure to get regular full body examinations from your dermatologist so any suspicious lesion can be caught early and biopsied.
Yes. Having one type of skin cancer does increase your risk of developing others.
Melanoma . Skin cancers are linked to increased sun exposure and tanning beds. There are strong genetic components as well. You are statistically more likely to develop a melanoma in your lifetime having a history of basal cell. See your dermatologist for routine skin exams, reduce sun exposure, use sun protection , conduct self skin exams monthly.
Yes. Skin cancers are usually due to sun exposure. Having a non-melanoma skin cancer increases the risk of developing melanoma. Here is information from the national cancer institute.