safelife:
You may fly the missed approach in NAV, provided the nav accuracy doesn't drop below 1.0 NM.
If it does (likely only if no DME-DME update possible) you would have to go on heading and follow conventional navigation.
That is correct only if the selected line of minimums is no less than RNP 0.30 and the missed approach does not require RNP of less than 1.0. Otherwise at least one IRU is required for the missed approach or extraction.
I don't think there is a GPS RNAV approach with only GPS based missed approach segment, that would leave you with no option in case GPS failes. Which is possible even with positive RAIM prediciton as it could be switched off or just fail.
Sure there are. But, the approach in such case does not require RNP of less than 0.30 and the missed approach doesn't require RNP of less than 1.0 In such case the missed approach will splay essentially like a conventional RNAV IAP. If you are in a remote area you have to DR the missed approach if the GPS signal fails. There are quite a few basic RNAV IAPs in remote areas that have no ground-base nav backup. Take a look at KBIH:
http://aeronav.faa.gov//d-tpp/1403/05737RR30.PDF
This approach does not require IRU redundancy and there is no requirement that the BIH VOR be operational to fly this approach.