Most of the time. Some people would be too sensitive to these chemical hair removers. Timing is important, too. They can be quite irritating if left on too long, especially on sensitive skin like the face. Definitely want to avoid applying on mucous membranes also.
Can be. If you mean nair/veet which are agents for hair removal, it depends. You can have a local reaction to them. You can get a chemical burn and skin discoloration. Also, certain skin areas are more sensitive than others. The face is very susceptible to irritation from harsh chemicals. Pigmented skin is the most sensitive and can be discolored by these agents.