If you are needing an internship strictly related to design, you are probably looking for a Professional Internship. This is something YOU need to apply for and you should know that they are very competitive, so I wouldn't bank graduation on it without a meaningful backup plan. In fact you may want to see if a College Program roll is acceptable for your school, because those are easier to land. Some areas, especially Imagineering, take PIs with no Disney experience if you have the right qualifications, but for some areas you are all but disqualified if you have not previously done a College Program in a more "front line" type role.
Does Disney keep interns? It varies a lot by area. In Imagineering they tend to keep successful interns if the project they were working on is continuing, but they tend to make them "independent contractors" meaning you are self-employed and contracting yourself to Disney. Sometimes you can maneuver your way into a true Disney role from that position, sometimes you end up out on your butt.
In other areas it depends, but no internship offers a guaranteed full time job. It's on you to network and apply for internal job postings. Occasionally you get lucky and pulled into a "statused" (permanent) full time job if the stars are lined up. Other times you may get on as a "TA" (temporary assignment), meaning your job has an end date where they can extend you, status you, or let you go. Often times this is them trying you out to see if you fit or it is tied to temporary position funding. Some PIs end up applying for a "front line" role after their internship (even though it's a pay and prestige cut) and hang out for a while in that job, applying for positions that will help them climb back up the more permanent ladder.
Disney can be a great internship opportunity. If you don't stay with Disney after an internship, don't count on a lot of nibbles in the Florida job market. Universal grabs some, but washed up Disney interns are a dime a dozen. But you take that resume item elsewhere and it impresses people.
