Hello Jessica!
You have some great questions there but, let's start with congratulations on your first trip to Walt Disney World!
If your sister has her heart set on seeing the princesses, the best and tastiest way to see them is to make a reservation to dine with Cinderella and her friends at Cinderella's Royal Table or at Akershus Royal Banquet Hall in the Norway Pavilion at World Showcase in Epcot. To make dining reservations, book online or call (407) WDW-DINE or (407) 939-3463 up to 180 days prior to your visit.
You can also find the Princesses throughout Walt Disney World. Don't miss the Rapunzel experience at the Magic Kingdom with personal interaction and involves some story time and drawing (Rapunzel's favorite pastime)! When you arrive at the Magic Kingdom in the morning check the times guide of when the first meet and greet is. When we were there in early December, the first experience started at 10am. You will want to be one of the first in line for the interactive experience because, the first 10 -20 children get a little extra time with Rapunzel and Flynn. I won't spoil the surprise but have your camera ready!
The cost of four tickets will vary depending on the type of tickets you buy. This link will provide the options for pricing the Four tickets. Walt Disney World is open 365 days a year so you should not worry about getting there and the park being closed.
As always, make sure to check the Times Guide at Magic Kingdom for character appearance locations, parade, and show times. If you cannot find the character you are searching for, go by Guest Services and ask a cast member if they can call the "Character Hotline". Hopefully, they will let you know where they might be located. I hope you and your family have a Magical Time at the Walt Disney World Resort! Thanks so much for your great questions!