Do they validate parking ticket if only going into downtown Disney.

Yes they will, with purchase.

Yes they do validate your parking for purchases over $20

Yes

I think so.

You get 3 hours of parking when you make a $20 minimum purchase and receive validation from any Downtown Disneylocation (including quick-service restaurants, merchandise locations and kiosks)—or up to 5 hours of parking with validation from anyDowntown Disney table-service restaurant or AMC Theatres movie experience.

In my experience they did.