For the COVID testing, it depends on your vaccine status as far as Royal is concerned, as well as the length of your trip.
For cruises LESS THAN 10 NIGHTS:
Unvaccinated: YES
Vaccinated: NO
I haven't heard anything in regards to B2B cruises or transatlantics, so I can't comment there.
However, it also depends on where you're cruising from or where you're going. That's determined by the local authorities, as are mask mandates, not Royal.
As far as check-in is concerned, you can usually check in online about 45 days before your cruise. Once you check in, you'll be able to pick an arrival time, please stick to this as it will help the Port Authority workers tremendously.