Got a reply by phone:
1. Checked bags: depends on checkin, 12.05 hours is borderline and they might not do it;
2. Most probably yes, VISA is required for layovers >= 12hours so this is the case;
3. Yes, it is possible to stay airside provided that 1 is True.

It is also true that given those 5 extra minutes, the moment I will walk through passport controls the timer will be <12 hours so technically they cannot force me to get a VISA but I guess the check will be done by the MRU CA.

As such this is not the best situation possible, I still need to understand what to do. Probably this is the reason why the flights do not show up in the website but just in the "multi city" trips section.