Auto-immune. An autoimmune disorder affecting the nasal mucos is more likely than cancer. You are urged to see your doctor to get an evaluation and forestall complications.
Not likley. Nasal cancer or nasopharnengeal carcinoma ocurrs deeper within the nares. This sounds like it could be a viral skin infection, especially if it is on the outside of your nostrils. The best thing to do would be to see your doctor and get it looked at, preferably when the lesions are present.
Not likely. This cancer is seen in the far east and mediterranean. It has a distinct histology, nonkeratinizing undifferentiated carcinoma with infiltrating lymphocytes called lymphoepithelioma, due to epstein-barr virus. The lesions above might be due to an infectious/viral cause. If they persist, a good otolaryngologist can be of help.