Can a GPS with compass, heading & groundspeed capability be used legally
in
lieu of a separate compass and airspeed instruments on an experimental
homebuilt airplane? Or at least in lieu of the separate compass?

You definitely need the airspeed!! Winds can make a GPS groundspeed pretty
far off and useless for airspeed deductions that you'd really want on
takeoff and landing.

As for compass, that's got to be in the FARs somewhere, too, likely 91.xxx.
On the other hand, given how good GPS course readouts are, I'd love it if
ATC would let you fly an assigned course, not just an assigned heading.

Ed Wischmeyer
ATP/CFII