transferring files to new Macbook via iCloud

On my old Macbook Pro I have the desktop, documents, and downloads folder all set up on icloud. Today I got a new Macbook Air. I will be using one computer at work and one at home, so I want my Air to have the same files as my Pro. I signed in to icloud on the Air, but my icloud files aren't showing up. When I click on Icloud in the Finder sidebar nothing shows up there either, just empty folders. I tried a different route and went to icloud.com. My files are all there, but the "download" button is grayed out, so I can't download any of the files from there either. Any suggestions?

Also, once I figure out how to download the files, is it possible to only download certain things? I know the Air has about half the space of my Pro, so I don't want to bog it down with unnecessary things.

Lastly, (and please excuse the ignorance, but I'm trying to wrap my brain around sharing the files between computers) will it work like Dropbox and other cloud services in that when I change a file on one computer it will automatically change it on the other computer as well?

Thanks for your time!