Where in the FAR or AIM is a high speed taxi defined?
There's no definition in the AIM or regulations, as far as I know, but there is one in the P/CG, sort of (emphasis mine):


  HIGH SPEED TAXIWAY− A long radius taxiway designed and provided with
  lighting or marking to define the path of aircraft, traveling at high
  speed (up to 60 knots), from the runway center to a point on the
  center of a taxiway. Also referred to as long radius exit or turn-off
  taxiway. The high speed taxiway is designed to expedite aircraft
  turning off the runway after landing, thus reducing runway occupancy
  time


So at least as far as the FAA is concerned, a high-speed taxi may be up to 60kts.

As for requesting it, you can request more or less anything. There's an active EAA chapter at my local airport and pilots who are in the process of building and testing aircraft sometimes request a high-speed taxi on the runway. The controllers don't question it or set any speed restrictions, it's all on the pilot. I suppose if things were busy they might deny the request, but the pilots know to do these things at quiet times anyway.