Yes, you are correct. Here in Canada we would:
a) Loss of RNP capability before starting an RNP approach
Advise ATC and request a traditional or visual approach.
b) Loss of RNP capability before reaching the FAF
c) Loss of RNP capability on final approach
This depends. In radar and non-terrain critical cases, you can continue with the field in sight - just advise ATC. They can then issue you a visual approach clearance so that you can get alternate missed approach instructions. If you're IMC, execute a missed approach and ATC will issue radar vectors and a climb to at least the minimum radar vectoring altitude.
If you've lost capability before the FAF
and you're flying a parallel RNP approach, then you have to advise ATC who will give you breakout instructions (a heading and an altitude).
If you're unlucky enough to be in a non-radar environment and you're in the mountains, I would suggest you follow your terrain recovery procedure and haul your butt up to the MSA. Pronto. Hopefully, you still have GPWS information to help you miss all the red and yellow spots. If not, do you have a weather radar that can be set to MAP mode and a co-pilot who can do it for you? Failing all that, you should have your approach chart. If you know roughly where you were and your speed, you can use that knowledge to avoid the hard stuff. We fly a few approaches like this at my airline, and I've certainly asked myself "what about now" through a few of those approaches. It's amazing how a little rain, ice, and/or turbulence can make those questions occur much more frequently.
The same goes for the question Jonty posed: what if your missed is RNP dependent? Here at our computers, I'd argue that is a highly unlikely situation and is the whole reason it is required work at my airline to check both the RAIM NOTAM and the RAIM through the box. Sitting in the airplane when that situation presents itself, who cares if the missed in RNP dependent. It's time to get out of Dodge by the most expeditious means