Moved to California from IL, have questions about registering my mopar in CA

Here's another suggestion, go to your local SoCal AAA office and join up. You can do all of your DMV paperwork through them without wasting half of your day standing in line.
My current '69 Dodge Dart project was an eBay buy brought in to California almost 4 years ago. All I needed to do was fill out a couple of forms and get the VIN verified by a police officer. Your local PD may or may not do this. Mine wouldn't, but my wife's nephew is in the Long Beach PD so he signed it off. I took the completed paperwork back to AAA, paid the fees and was done. The only visual inspection my Dart ever got was VIN verification.
I don't know what your license fees were like in Illinois, but be prepared for California.