1. Can't help you there I'm afraid, perhaps a regular in MEX can comment on food there.
2. You can eat when you like in F. So you can ask them to serve the meals in a different order from the usual - just make it clear what you want later so they keep it for you. I have, for example, reversed the small and large meals on a daytime flight. F has ample catering on all flights. In your situation I would consider eating some of the "breakfast" before going to sleep then wake up and eat the "dinner" as a brunch before arrival.
3. You won't have too long but you ought to be able to get yourself a shower over in T3 GF and some food. Shower wait should be minimal. T3 GF is nice (nicer than the T5 GF) and overall you aren't missing out on much of the arrivals lounge experience when you're getting most of it in T3 GF. With a 2 hour connection I wouldn't risk going landside in any case.
So I think you can have pretty much as F an experience as you can from most other outstations, bearing the above points in mind.