If the aircraft is fitted with an IFR certificated GPS as part of its fit, then, yes, you can fly GPS approaches. RAIM, per se, is not required if the GPS is integrated with the FMS - the integrity function is part of the FMS.
I don't know why you would want to manually deselect satellites -GPS only uses the "best 4" for the navigation solution anyway - any others available are used as for RAIM.
There are RNP0.3 approaches available outside the US.
AFAIK, nothing below that figure - yet. Some airlines are looking for NG special approvals down to RNP0.1