What classes could I take in college to teach me about cars and how to build a solar powered car by myself?
Forget about the fashionable part, get it working first. Besides a working model, no matter how klutzy it is, will be attractive for someone. Leave that for the second model.
Use an existing car, something very light. You can buy electric car conversion kits on line. Start with one of those. Then add as much solar cells as can fit on the roof of the car and connect them to the batteries.
You do realize this will not work on cloudy days. Also, the solar array will be a target for theft.
If you are aiming at a manufacturable product, you will need several people at least.
If it’s just a hobby, study up on the electronic aspects, batteries, motors, solar cells, computer controllers. The mechanical stuff can be handled by any good car mechanic.
I know a mechanical engineer who built his own electric car. He started with a SAAB sonnet, a small sports car. Put in a lot of lead acid batteries and an electric motor. Took him a year or so. He had help with the electric parts.
How do solar powered cars save money?
That’s the only way they save money and preserve the nature through not using gas.