A lot depends upon your age, physical condition, hydration, and circulatory status. For a younger person in good health there should be no problems. For someone over fifty, I would get a physician's approval. The comment about being well-hydrated is well-taken.
no is not.profesional swimmers do that all the time.but not more then 3 times a week.
I would assume not - hot and cold therapy is typically used for healing; just so long as you're hydrated - why would you think it could be unhealthy?
depends on if you are getting acne or infections otherwise go for it