Other North & South America Frequent Flyer Programs - CUN-MEX (on AM) + MEX-CDG-SIN (AF) same day transit questions

I've booked 2 flights on different airlines that connect at MEX Airport on the same day, but transit at different terminals and is not a tight connection (which may save some trouble)

My Aeromexico CUN-MEX flight arrives at 1600h (AM444) at MEX T2 (not known whether it arrives at T2 North or T2 South) and I'm connecting to the CDG bound Air France flight departing MEX T1 (International) at 2330h (AF435)

some questions I'd like to ask, since it's my first time doing connections on different airlines

1) what are the procedures for a domestic-to-international transfer in MEX Airport, particularly when I've to use both terminals?

2) will my checked luggage be through-checked from Cancun to Singapore by AM? Bearing in mind that I'm transferring from one SkyTeam partner to another.

3) I'm taking AM Domestic Clase Premier from CUN-MEX and AF International Voyageur (Economy) on the MEX-CDG-SIN. is lounge access possible at MEX? or have to pay for a day-pass..

The T2 domestic pier is the south pier, but that doesn't really matter. You will arrive at domestic arrivals and exit to T2 landside.

Upstairs, there is a tram to take you from T2 to T1. Note that they won't let you board the tram without a boarding pass or itinerary print-out for the other terminal, so have that in hand.

You can probably have your bags interlined to AF in MEX, so ask AM in CUN to have them checked through. If you want to be totally safe though, then claim them in MEX T2 and take them over to T1 with you. (This is what I would do ;) ).

There is an AM lounge in T1 that AF uses; standard SkyTeam access rules apply.