Is it possible to get skin cancer even if you always were long sleeves and SPF 30?

Yes. Uva and uvb are both potential risk factors, but ultraviolet radiation is not the only cause. There are many different types of skin cancer, with sun exposure related more closely to the most common types -- but not to all of them.
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.