Never been on a cruise. Is dressing formally required or are there areas where you could still go/eat and be dressed casually?
Yes to both, sort of. There are "formal" nights on every cruise, either one, two or more, depending on the length. While formal attire is encouraged, evening gowns, tuxes, etc are not required, and I've seen those, down to just sort of dressy attire. That's just in the main dining room, and perhaps the speciality restaurants. The rest of the time, you can simply dress "nicely"
And if you don't choose to partake, there are definitely other options for dinner on the formal nights. I myself enjoy getting dressed up each night, a bit more for the formal nights, and going to dinner. I don't really do that at home. But others do not.