Yes, yes and yes. Now on the 3 night cruise's you won't see as many people dressed up in the dining room, but for the 4 night and longer you will. The Dream actually has two seperate pirate parties. One with the characters in the early eveing and one later on where they also have the fireworks (and I swear they had more on this ship than they did on my last Wonder cruise 5 months earlier). I wear black jeans, boots (if it's a winter cruise) and or black shorts and sandals (if it's a summer cruise) along with my black pirate t-shirt. They gave out pirate bandanas this time on the Dream with Mickey heads on it, so between that and my other accessories...I'd say I dress up. This time I did a quick 3 nighter, so I changed after my early seating and then went to the second pirate night. You'll some folks dressed up and some not on the Dream. I think more people participated on the older ships, but I am sure it will catch on soon on the new ships as well.
As for dressing like a princess...oh you can't get any more adorable than a little girl all dressed up and that sure would fit the theming in the Royal Palace dining room so I'd say go for it. On the new Fantasy ship they will even have that little boutique they have at Downtown Disney, so your princess can get their hair done to match.
9 Disney cruise's and counting...rebooked for the Fantasy.