White spots in mouth are cancer, right?

Usually not. There are many causes of white spots in the mouth and most of them are not cancer. It is not possible to say if the spots you have are cancer or not, without examination and if indicated by a biopsy sent to a pathologist for microscopic study.
Not quite. Exam, history, and biopsy will help with answer. Smoking, smoke-less tobacco, history of radiation to head and neck may increase risk for oral cancer. See oral surgeon.