I can’t imagine you needing more than 5 projects covering all stages of the design process for getting into a degree. I’m not American so I wouldn’t know that for sure there though. Definitely suggest playing with OnShape and also getting a free 30 day trial of Keyshot later in your experimenting. Photoshop and Illustrator are available on 30 day free trials too, and GIMP, Inkskape and a number of other programs are pretty good free options too.
One thing I will say is being enthusiastic at the interview and showing that you understand what Product Design is and why it is necessary are as important as any tangible skills or theoretical knowledge.