The "formal" evenings aren't usually all that formal. Even on the black tie evenings, plenty of men were in the restaurants in shirts/trousers rather than suits, jackets and ties. As long as you're smart (i.e. no shorts, t shirts, jeans, etc) you'll be fine. We were really worried and OH took his jacket/tie etc but never bothered wearing them.
The weather will have to be really bad for sea sickness. In normal situations you can barely feel it moving and even in rough seas it's usually just a slight rocking motion. The stabilisers etc usually do a cracking job of keeping it smooth.
Re drinks, water/tea/coffee is often chargeable in the bars and waiter-served restaurants but free in the buffet restaurant.
Re cleanliness, yes, as others have said, wash your hands all the time. Our ship was spotlessly clean, with cleaners constantly going around wiping handrails, door handles, etc., but you just never know. In the buffet restaurants, just be cautious and not take food that looks like it's been handled by other passengers, i.e. anything that looks like it's been moved in the serving tray. If you're paranoid, choose from "full" or nearly full trays that will have only recently been put out. The buffets are usually so busy that some trays are only out a matter of minutes before they're empty and being replaced!
Your ship may have an "app" or an option to view your onboard account on the in-room TV, so good idea to keep checking it to see what you're being charged for, rather than waiting until the end and finding a huge bill.
Like you, we were worried for our first cruise last year, took far too many "posh" clothes, worried about travel sickness, worried about norovirus, but it was all fine and we can't wait for the next.