Welcome to CC.
There should be free sessions in Europe the same as in the US - you might confirm via the app (set to current sailing). Any Key specific perks/sessions should also be the same.
That (the AC being off while door is open) is also true on most RCI ships, but the open door does affect the cabins around you when you do that. @chengkp75 may have some insight if the infinity veranda HVAC design is any different than current ships.
That’s why I said if you have a good connection to a Wi-Fi access point - once you have a good local connection, the internet performance itself has improved a lot. Grandeur had the old geosynchronous satellite internet so the performance improvements were great (if you can get connected).
Assume shows around dinner time are aligned with the timing of early and late traditional dining. If you want an idea of what to expect, look in the app for your ship and closest in sailing similar to yours.
The cash option seems to have been removed from check in so if you plan to complete check in, you will need to supply a card. You can then change that to cash on board.