1) Yup, it's a definite must to keep in contact with others -- outside of the ship.
Within the ship, you could technically use their app that allows you to message others within the ship who are also using the app. It's just a simple messaging app, so it's not like a Whatsapp equivalent, but it's a free way to keep in touch as long as everyone you want to keep in touch with on-board is a Royal Caribbean member, has the app downloaded and has configured it keep in touch with your family (i.e. created a group, chat or chats that you need like one with everyone in the fam, another only with your other half, another only with your kids, etc. -- the choice is yours)
You can't rely on roaming data while onboard -- the ship will be far away from land-based telecom towers to be of any assistance.
2) The Royal app by Royal Caribbean. Everything you want to do like plan activities, check schedules, book stuff, and even chat is on it. So it's a must have and it's one of those things you'll be reminded to do before embarking on the journey.
3) Haven't tried those 'unlimited dining packages' but basically, it's no different from the 'unlimited drinks' package and the likes where you get more mileage out of these if you're a big eater/drinker, OR you don't want to keep count on what you want to dine on. Basically, it's the easy way out to have access to all kinds of meals without thinking as the ship has many pay-per-pax/dish based restaurants in addition to your free options that are included with your ticket to come onboard.
IMHO, don't think you need to take up the package assuming the free options are adequate (and they generally are) and only pay for selective paid dining if you want to amp up one of your lunch/dinners onboard.
4) Usually this was handled by room cards issued, but I've not been on an RCI cruise in the last three years, so things may have changed.
5) There's too much variety on this note -- from entertainment, shows, to just lazing around

Your daily planner that will be sent via the app will have a list of activities like classes, group activities, puzzle solving, bingo, and much much more. So there's a lot to take in if you're going onboard for the first time. I don't think there's a must-do/must-see first kind of thing, but I'm a seasoned cruise user, so my view would vary based on ship brand and class
6) If you're going with fixed timing on the main dining venue -- everyone has a seat with service staff to assist. There's nothing to worry for that. If you're thinking of using Windjammer (their buffet place), then it's the usual lunch and dinner timings where you'll see peak usage and if you come earlier or later than that, the crowd will be less.
Have a great first-time cruise trip!