Is it possible to get skin cancer even if you always wore long sleeves outside?

Yes. Clothes provide a false sense of safety. Actually, the sun's rays still penetrate clothing. Nothing prevents skin cancer other than avoiding the sun altogether. There are special fabrics and clothing that are 30+ SPF and higher made to add protection if you are active. I would suggest this option if you are outdoors for long periods of time in the sun.
Yes. Long sleeves cover arms and would provide protection to those areas, however, long sleeves would not protect from skin cancer developing on the face, scalp and other areas.
Yes bit less likely. Skin cancers are due to cumulative sun damage...Accrued over a lifetime.