making a search box- is it possible?

I'm going to make a community for highschools, so instead of making a long list with all the highschools I want to create a search box. Is it possible? Should I use fields builder for that?

Well, yes, I would say the page buider/field builder would be one way to go.  You could put your form code in an HTML block.

As for the the actual backend search engine, that's the tricky bit.  I don't think there is one natively in Dolphin.  You could look around for a mod.  You could maybe write one yourself - a simple code you might be able to find online.  Or you could try adding a Google search or similar to your site, but you'll have to rely on whatever search engine to index all the pages you want to search, which may not happen.