This is like opening a can of worms. Hopefully this thread stays on track.
I agree, B-D-A would be an illegal route to file IFR since point D resides outside the known VOR ranges.
I agree, B-C-A would be a legal route to file IFR.
I could be wrong on this one, but I don’t think B-E-A would be a legal route to file IFR. Even with DME, that wouldn’t be enough to navigate to point E using VOR navigation only.
I also want to clarify that all of these routes can be flown legally using GPS so long as the GPS is up to date and all waypoints have been verified against a current chart. These questions are specific to the legality of PLANNING.
Onto the next section:
Quoting you, “ MY INTERPRETATION, ASSUMING AIRPLANE HAS A NON-WAAS (TSO- C129 or TSO-C196) GPS…
AND, IF THE GPS DOES NOT HAVE FDE (MEANING 6 SATELLITES AVAILABLE) ANY GPS APPROACH IS NOT AUTHORIZED
QUESTION: IS THIS CORRECT?”
Your interpretation is incorrect. Without FDE, you would still have RAIM. That said, remember that the question is asking about PLANNING. Once enroute, you can fly whatever approach you want so long as you are current and the aircraft is equipped.
Scenario 1 is legal per “…may file based on a GPS-based IAP at either the destination or the alternate airport, but not at both locations.”
Scenario 2 is legal for the same reason in Scenario 1.
Scenario 3 is not legal because an alternate must have an instrument approach. In scenario 3, the alternate must have something other than a GPS approach since a GPS approach was planned at the destination…or…if the destination has an ILS or LOC or VOR approach and planning was based on any of those, then a GPS app at the alternate would be legal to PLAN for.
Clear as mud?
Disclaimer: I am not an Instructor anymore and I have not taught since I left ATP in 2017. I could be wrong. Check your own sources.