Looking for Answers about Canada & New England?

Sure you can --- but why would you want to???

It should be fine if you have a couple of bottles of soft drinks but I doubt they will allow whole packs of soft drinks.

NCL has a BAGS program where they will deliver and check in the bags for you directly with the airline. There is a cost associated with this program and the program is limited to certain airlines.
Check on NCL's website for further details on the program.
http://www2.ncl.com/freestyle-cruise/bags

Yes. All staterooms have refrigerators.
The amenities the ship's stateroom is just as in any hotel. Fridge, TV, coffee maker, ice buckets, beach towels, mini-safe, alarm clock, hair dryers, soaps and shampoo.

You are cruising Freestyle. There are no assigned times or seats for dinner. Just as in a regular restaurant, you can go anytime the restaurant is open and the seating is on a first come first serve basis. The restaurants are usually open for dinner from around 5:30 PM to about 10 PM.
You cannot make reservations for the main dining rooms. The specialty restaurants do accept reservation.
As far as shopping is concerned, there are is a shopping area with some shops but not a big selection.