Let's try to answer your 4 questions one by one.
(1) There's different soda card programs available. Whether it is worth it or not depends upon how much they drink, and their ages. Here's a link to NCL's soda carda:
Children's Soda Program (ages 6 months - 12 years old)
Unlimited Fountain Soda
Includes: Coke, Diet Coke, Sprite, Ginger Ale, Tonic Water, and Soda Water. Prepaid @ $4.00 per person per day x Cruise days plus 15% gratuity
and applicable taxes. Souvenir Thermal mug included in the purchase of the program.
Adult and Teen Soda Program (ages 13 and older)
Unlimited Fountain Soda
Includes: Coke, Diet Coke, Sprite, Ginger Ale, Tonic Water, and Soda Water. The entire cruise must be purchased. Non-Refundable. Prepaid @ $6.25 per person per day x Cruise days plus 15% gratuity and applicable taxes. Souvenir Thermal mug included in the purchase of the program.
Teen Passport Program (13-17 Years of Age) $34.50
20 non-alcoholic drinks, including non-alcoholic smoothie in a 12-14 oz. glass.
The teen and a guest are entitled to an afternoon dance party with the D.J., pizza and unlimited non-alcoholic drinks. The Teen will also receive an invitation to a "Farewell Frat Party" on the last evening of the cruise. Passports are not replaceable if lost.
***Purchase of this package does not serve as the required registration for the Teen Program's activities. A parent or guardian must register their teen by seeing any member of the youth staff once onboard.
The Kid's Crew Backpack includes the Kids Soda Program.
3-day cruise package $30.50
4-day cruise package $33.00
7-day cruise package $39.50
(2) In the buffet and the restaurants there will be free glasses of water, ice tea, milk, and juices available.
(3) Free public beaches are within walking distances from some of the islands, but not all.
I suggest surfing to a port of call forums to discover which.
(4) The Sky does NOT have a self service laundrymat. It does have valet services using a ship's laundry. Here's an old Valet Services order form, although the prices should be similar this year.
On longer cruises, NCL usually has a fill a laundry bag special for $20 once. For the Sky's shorter length cruises, I'm not sure whether they will have it or not. We'll have to wait to hear from passengers from its first few cruises, which start next month.