According to the rules of professional tennis, yes. Many female players have used double-handed strokes on backhand shots.
You could quite possibly switch hands during a match. But if you are an advanced player and not just playing social tennis, it would be quite an insensible thing to do.
Very few players are ambidextrous, mainly because of the many hours of practice required just to learn how to use one particular hand effectively.
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It's perfectly acceptable to use both hands, either together or separately, in tennis. There are no rules proscribing the practice.
No because if your wrist strap is removed, it is an automatic equipment violation and your opponent will be awarded a point or side out.
If you mean 'changing hands' as in changing from using your left hand dominantly to your right hand dominantly (or vice versa), then you can. There isn't a rule against it.