No, it is a violation in High School rules, Rule 4.29 in the NFHS rule book says
"Kicking the ball is intentionally striking it with any part of the leg or foot."
The rule book doesn't specify the difference between the offensive or defensive kicking. So any party doing the above action would be called for a violation.
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Yes. It is not possible to travel while dribbling. The height of the dribble is also irrelevant.
If a player in Basketball travels, the umpire calls travel and its a turn over to the other team, meaning the other team gets the ball and they throw it in from the side line.
If you are in the air and dribbling at the same time it is insanely awesome but not traveling.