In chickenpox, is it safe and beneficial to use betadine solution on the skin including the face to ease itching? can it be applied to the scalp too?

I wouldn't: Betadine has the potential to sensitize you(make allergic) to its components if it is left on the skin for indefinite periods. I make great effort to remove any trace of it after I use it to sterilize an area for a procedure.

Chickenpox: I agree with Dr. Ferguson about use of Betadine solution. Itching can be soothed with Calamine lotion & colloidal oatmeal baths. To reduce infections from scratching blisters – keep fingernails short.