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

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: 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 bit less likely: Skin cancers are due to cumulative sun damage...Accrued over a lifetime.