Someone on the Crown currently has posted a few Patters( newsletter). Here is the dining times for Crown Princess. May 7 which was the embarkation day in DaVinci dining room open from 7 AM to 9 AM for breakfast, noon to 130 for lunch, and 5 PM to 930 for dinner .
day number two which was a Sea day the same times. Michelangelo dining room says it’s closed . Boticelli dining room for both of those days said 5 PM to 9:30 PM.
Day three May 9 in Ketchikan -da Vinci dining room open 7 AM to 9 AM for breakfast and then 5 PM to 9:30 PM for dinner.
Day four which was May 10 in Skagway -da Vinci dining room open 7 AM to 9 AM for breakfast, noon to 130 for lunch, and 5 PM to 9:30 PM for dinner.
I didn’t look that carefully at the Boticelli dining room ,but I have a feeling it was open every evening from 5 to 930pm.
All the dining rooms except for specialty will serve the same menu for dinner. Nothing special that I know of on first night.
As far as taking your carry-on to your cabin on embarkation day ,it really depends on what time you board,but rooms can be available at noon time to 1 PM .sometimes the fire doors are closed and you cannot drop off any luggage .sometimes they’re open & your room is ready, you just never know exactly.
Take a look at the current sailing ( posts)of the Crown-and you can probably look at it more in detail. Title says live from the crown return to service May 7