First, take the Cruise Critic opinions with a grain of salt. The way some people there follow their cruise lines can be cultlike.
1.) I can’t speak for Norwegian, but I’ve cruised Holland America and Princess. Holland America had only traditional dining (Early and Late). Princess had Early and Late Traditional, and an option for “Anytime Dining.” In Traditional, you have the same table, same servers, and same tablemates at the same time every dinner. With “Anytime” you walk in like a regular restaurant and you’re sat at a random table with random people. Unfortunately, though I believe they do quite a good job with lines, this also means a possible wait if you come at peak times. We’ve never done “anytime” since the formal dining is one of the highlights for my mother. However a tablemate with 20 or so cruises under her belt said an astonishing number of people never even see the formal dining room. They eat exclusively at the buffets and pizza type places. Also, IIRC, some cruise lines are moving towards Anytime Dining being the standard.
Ships usually offer multiple dining options. There is the random eateries around the ship (pizza, burgers, buffet) that may be open during certain hours, there is the formal dining (formal meal), then there are the special restaurants that you must pay a premium. Food quality was just decent. Nothing bad, but nothing blew my socks off either.
2.) Allegedly, there were 5,000+ people on my British Isles cruise. I say “allegedly” because I swear we never saw more than a few hundred of them. The ship is HUGE and the shows are the only time I ever saw more than just a handful of people. Doesn’t feel crowded AT ALL.
3.) There are usually shows every night. They could range from comedy acts to very traditional broadway revues. The cruise lines run games trivia contests, bingo, there’s usually a sign up sheet for people who want a game of bridge or chess, etc.
How open minded are your parents? You should check your cruise line’s policy regarding drinking and gambling. I believe the age to gamble was 18. Drinking age was 21, although on my first cruise on Holland America I was only 20. I ordered a Brandy and they brought it with my mother’s permission.
They may have some kids things for your younger sister and kids her age, but it sounds like you guys have a sizable group and you’d have to be careful she doesn’t just feel abandoned.
*I wouldn’t worry too much about entertainment. Unless you have multiple sea days, you spend most of the day ashore. By the time you get back to the boat you eat dinner, drag your ass to the show, then pass out from exhaustion the second you hit your state room.