Mariner of the Seas is getting A LOT of upgrades for summer of 2018, so based on your sail date I don't know what you will have but here are some basics:
Communication - only the newest ships (not renovated ships) have apps where you can text each other. You either have to use short wave walkie talkies or purchase the internet package and use an internet based service like facebook messenger, etc.
Food - The Windjammer is a buffet for all 3 meal times and has plenty to offer if you don't want to go to any sit down restaurants. There will also be food available at at least 1 cafe area no charge for pastries, pizza, desserts, coffee, etc 24 hours.
Drinks - the items you listed are always available. Read my other reply regarding tumblers.
Kids - If you surrender your children to the care of the kids club staff they will always be under proper supervision. I don't know if they take them outside or not, perhaps someone else can help you in that area, we didn't take our kids until they were in their late teens.
Hotel - I'm sure any inexpensive hotel will do. I would ask if any of them allow you to park at the hotel and take a shuttle to the port. That would save you the port parking fee.
Online Check In - This is done to prefill your identity information (passport info, etc). It is most of your paperwork. A few weeks before your departure date you will also get your SeaPass document. This is the main document you print out for 1 representative in your stateroom for check in purposes, and includes the credit card info for any onboard purchases. You will never pay with cash or credit card onboard - all purchases will be via SeaPass cards and charged to your master account. You can arrive at the port any time after the standard boarding time, I like to arrive between 12-1pm so I can get access to the ship as early as possible.
Coco Cay - For your younger kids I highly recommend you pay for access to the floating water park areas. It is an extra 'excursion' fee, but your kids will have a blast!
Movies - There is an outdoor movie screen that plays movies throughout the day, and sometimes movies are played inside one of the theaters.
Lastly, as I said earlier, Mariner is getting upgraded for this summer so none of us will be able to say anything about your ship specifically, just what we have experienced on others. I have been on 5 ships so far, and some aspects are the same, but there are some unique things about each ship too! It looks like Mariner is getting some cool waterslides and more for some extra onboard fun.