I understand that 250 kts below 10,000 ft is a law and ATC cannot approve it except in an emergency so if there is an incident you are held accountable if you were exceeding 250 below 10,000. When ATC approves high speed climb or descent below 10,000 ft all he is telling you is that there is no conflict with traffic.
Depends in which States airspace you are flying. It is legal in many places.