Congratulations on your anniversary! Quite a milestone, and a cruise is a great way to celebrate.
There will not be irons & ironing boards in the rooms, due to potential fire hazard. (Cruise lines don't want you to bring your own either.) I don't believe Rhapsody has self-serve laundry rooms, but you will probably get a more definitive answer from someone else on the forum.
"Formal" means different things to different people. You will see everything from long gowns and tuxes to "Sunday best." (And probably a few wandering around in their cutoffs as well, though not as much as on some other lines.) If you are used to really formal wear, and don't mind it, by all means bring it; you won't feel out of place. The ship's photographers will have various places set up throughout the ship for nice portraits that night too, and it's a good opportunity to get a nice picture done. (Extra charge, of course!
Have a wonderful anniversary!