thibautg78,
I can't say I have always been successful in my flight school's quality checks, but still I'd like to take an educated guess.
- LNAV and VNAV can be used simultaneously, and in fact they are during climb and descent. How else would you follow an SID or a STAR? However, VNAV is not usually used during cruise flight. Instead the APFDS is used in height lock, but this does not mean you cannot operate LNAV and VNAV together. So, the correct answer is "b".
- I'm not certain either. In an A320 an RA failure gives a single chime (i. e. an aural warning) and a master caution light (not a red lamp, as in the question, but still a lamp). Hence, I would tend to "c".
- The correct answer is "a" (independent mode). In single mode only one FMS is operational. I've never heard of dual or seperate mode.
Good luck with your assessment.