Hi, it always depends on the cruise line you go with. Formal nights are dressy nights, with gents always wearing jacket and tie. Some cruise lines have a dress code, others do not. Your booking agent should be able to help you, I have found that in the back pages of the cruise brochure it will suggest what to wear on formal, casual, or semi formal nights. \tours bought on board are always quite expensive, and a lot you can do yourself, but always remember, that if you are on a ship tour, you will always get back to the ship before it sails. On DIY tours, if you are not back at sailing time, the ship has no obligation to wait for you.
Treatments at the spa are usually expensive, but there is always plenty to do on sea days, this is always my favourite part of the cruise.
Just enjoy yourself, and remember nobody is going to turn you away from any event because you are not dressed to their recommendations.
Have a great time.