Navigraph + MSFS 2020 Flightplan

That is strange … Have you tried making your flight plan in MSFS (in Welcome - flight panning screen, and the saving it while there, before starting to FLY.
Then while in the Flight Planning page, make a different one, and then load back in the one you saved.

(1) Does the MCDU see that loaded in FP. ?

Make sure you have the LATEST LNM.
It was only recently that LNM was updated to create correct MSFS FPs, with the fixes associated with airport (ie Sids & Stars), being correctly entered, with their associated airport ICAO code.

Prior to that, those fixes without associated airport IDS, did not allow the correct Sids & Stars to be formed.

If you care to post a typical simbrief FP that you have that is not working, maybe I or someone else can look at it and see if we can spot what is going wrong.

It should work : Simbief ->- LNM ->- MSFS (provided you have the lastest LNM)