Hi Veronica!
Well, Princess weekend could be water park weather, you just never know. I am in Orlando now for the marathon and it is almost 90 degrees. A few years ago, it was 17 degrees! The average high in February is around 72 degrees.
You don't need a ticket at all to go to Downtown Disney. The Disney Quest building does require a ticket. You can buy a single ticket, or if you have the Magic Your Way Water Park Fun and more it is included. If you don't plan to go to water parks, then a one day Disney Quest ticket would probably be more economical. Here is the link to
Disney World Tickets.
Your family can watch you without having a ticket. My favorite spectator viewing area is inside the Magic Kingdom on Main Street USA. This is around mile 5.3 for the race. Spectators can enter the park and cheer on their runners. All runners and fans will be cleared of the park before it opens officially for the day. They can also see you at the finish line by taking the monorails back to the Epcot parking lot.
Crowds are usually very pleasant during Princess weekend. The Magic Kingdom is usually the busiest on that Saturday. Sunday is much less crowded, and the following week is very low. The week before the Princess Half is busier because it includes President's Day, which is a busy time at Walt Disney World.
I hope this information helps. Please let me know if you have any other questions!