Yes. Yes, but you are doing the right things. Make sure to reapply the sunscreen on a regular basis. A strong family history of skin cancers would be one thing in particular which would signify an increased risk of skin cancer. If this is the case, find a local dermatologist and get screened regularly based on his/her recommendations.
Yes. Sun is a. Cause, particularly of basal and squamous cancers, abd even the lethal melanoma, but its not the only cause. Inborn dysplastic nevus syndrome is another. Odd types (lypmoma cutis, merkel cell tumors, angiosarcomas) may have no identified connection with sun exposure. And sun blocks "reduce" do not eliminate risk.