here's the cut and paste from doc's, also answers the under class B issue... go faster if the A/C needs it no call no clearance
The rules regarding aircraft speed are contained in FAR 91.117. I will break this rule down into its parts and then answer your questions:
FAR 91.117 (with commentary):
"(a) Unless otherwise authorized by the Administrator, no person may operate an aircraft below 10,000 feet MSL at an indicated airspeed of more than 250 knots (288 mph)."
Comments: The "Administrator" is not ATC, and ATC has no authority to either approve or request speeds in excess of 250 KIAS below 10,000 feet MSL.
If the minimum safe speed for the operation requires a higher speed, the aircraft may be flown at that speed (see paragraph (d) below). Note that there is no requirement to request this speed or to advise ATC that you require this speed.
There is a test program at IAH (Houston) to allow speed in excess of 250 KIAS in the Houston Class B, but only for departures. It is published as a Notam via a change that was made through the exemption process (e.g. as approved by the Administrator).
As noted in paragraph (b) below, the rules for Class B airspace areas are the same as in pargraph (a). So ATC cannot waive this speed limit in Class B, except if authorized by the Administrator (e.g. as in the case of IAH).
"(b) Unless otherwise authorized or required by ATC, no person may operate an aircraft at or below 2,500 feet above the surface within 4 nautical miles of the primary airport of a Class C or Class D airspace area at an indicated airspeed of more than 200 knots (230 mph). This paragraph (b) does not apply to any operations within a Class B airspace area. Such operations shall comply with paragraph (a) of this section."
Comments: You cannot exceed 200 KIAS within 4 nm of the primary airport of a Class C or D airspace area if you are at or below 2500 feet above the surface. However, ATC can approve a higher speed.
Note that this does not apply in all of Class C (or D) airspace. It only applies within the stated distance and height limits.
Note that the Class B limit is as per paragraph (a), so ATC has no authority to waive the Class B limit.
As with the other limits, you can exceed this speed if the minimum safe speed is in excess of the limit. A courtesy call is a good idea, but you do not need to make one, nor do you need to request the higher speed from ATC.
"(c) No person may operate an aircraft in the airspace underlying a Class B airspace area designated for an airport or in a VFR corridor designated through such a Class B airspace area, at an indicated airspeed of more than 200 knots (230 mph)."
Comments: The only relief from this rule is when the minimum safe speed for the operation is higher than 200 KIAS. ATC cannot waive it. No need to request the speed or to advise ATC.
"(d) If the minimum safe airspeed for any particular operation is greater than the maximum speed prescribed in this section, the aircraft may be operated at that minimum speed."
Comments: You can fly the minimum safe speed without requesting it, and without advising ATC. In the case of needing to exceed 250 KIAS below 10,000 feet MSL or in CLass B, just make an advisory call if desired. No need to request the higher speed -- ATC cannot grant your request... As noted above, a call to the controller would be a thing to consider, as the controller will then be able to plan for yor speed, thus assisting him to separate traffic.
Your questions:
"Q 1. ATC requests best foward speed while below class B. What would you do?"
A: Fly 200 KIAS or less, unless the minimum safe speed was higher.
"Q 2. On departure (below 10) ATC says " delete 250 restriction or climb unrestricted or high speed climb approved". What to do?"
Unless you are in the IAH Class B airspace area, the controller cannot delete the 250 KIAS limit. If the controller tells you that high speed is approved, you should fly 250 KIAS or less until reaching 10,000 feet in the climb, then maintain best forward speed. Or fly the minimum safe airspeed until reaching 10,000 feet, then best forward speed at or above 10,000 ft MSL