There will be free soft serve ice cream, it's normally by the pool area on RCL (but I haven't been on Oasis). If you want hard ice cream, that isn't free if you get it at the shop (I think it's Cups and Scoops on deck 6 Oasis). But in my experience they also serve hard ice cream at dinner in the MDR and by the buffet at dinner, not sure about lunch, we never were looking for it then. My son loves the soft serve, and gets ice cream or sorbet every night for dessert. We also loved the milk shakes from Johnny Rockets (not free, they will give it to you to go).
Like I said, I haven't been on Oasis class, but if they ask for your room card, it's likely not free. There should be signage up as well indicating the price. There is usually a coffee place (cafe promenade) for a charge, but they may serve some snack items that are free. the Ice Cream store is a charge and clearly marked. There was also a cupcake store which was also not free. Some ships have a candy store as well, also not free.
Formal night is normally night 2 and 5 or 6 on a 7-night cruise, but it may change depending on your itinerary. It will be listed in the daily schedule, the style of dress for dinner (formal, cruise casual, elegant, etc). Don't feel you have to go over the top formal if you don't want to. I take a couple "nicer" dresses and put kiddo in a shirt/vest/tie combo. We are often more dressed up than others on the ship.
There should be a gym/fitness room. They will offer classes that I don't think are free, but also equipment that you can use that is free to use. I think it's on Deck 5, the Vitality Spa and Fitness Center.