cruiserccl

The Healthy Sail Center | Healthy & Safe Cruises | Royal Caribbean Cruises   A few days into the cruise you will be able to schedule your PCR test to return to Canada.
 
Dining reservations- super easy, go to any specialty restaurant when you get onboard, bring your planner/schedule with you.  Spend a few minutes with the staff at any specialty restaurant and they can set up the rest of your reservations for the rest of your cruise.  

For dining packages, you can book the times for dining when you board the ship. By then you will have the entertainment schedule on the app. Entertainment in the past has been scheduled around traditional dining room times of 5:30 and 8:00 PM. Anthem sometimes has matinee shows on sea days as well. 

Keep an eye on the cruise compass section on this website once she returns to Bayonne for updated cruise compassess.  
https://www.royalcaribbeanblog.com/cruise-compass?ship=435
From them you'll be able to see show times and typical event times.
I've cruised on Anthem twice in December and twice in January.  I'm more nervous about the plane having snow delays than the ship.  One winter storm can mess up flights along the East coast for days.  

I might go a tad earlier for dinner, but again, it all depends on the ship and exactly what shows are running.

Reserving the entertainment onboard is quick and easy and they gave us a flyer in our cabin that listed all the shows and headliner events for each day. We reviewed them with our friends and made the reservations and/or reminders on the app when we were logged into the ships WiFi. Very easy and with the reduced capacity there was not a show where we were turned away. It could be also that we did it early. They were checking that we had reservations but I also think they let everyone in once those with reservations were in. Dining reservations were also easy in the app. Only complaint is you have to go through several steps to make your reservations. They could have made it easier with a few less steps I felt were unnecessary but it sure beats the long lines of earlier cruises.

Usually shows run twice a night so either main dining room seating will give you time to see the shows.
Check out old cruise compasses  to get an idea 

I don't know if anyone really knows how long the onboard-only reservations will continue. But for dinner scheduling purposes, you could look at previous cruise planners to see what time shows typically have been.
https://www.royalcaribbeanblog.com/cruise-compass

Yes, that's typically the time frame. One early showing, one late showing.
Yes, it's the PCR test, they'll send info to your stateroom a few days before you have to schedule it.
We sailed out of Cape Liberty a few years ago. It was March, but it had dumped snow a few days prior - there were still massive snow drifts at the hotel we stayed at (and at the port) but we got off without a hitch.