Are there binaries for older versions of Cuba?

I can see GitHub and releases but I have tried building even the newest version and there is not enough information to even run it.

So I was wondering if there binaries with older versions somewhere? I do see a list of changelogs but nothing to download.

AFAIK, All versions are available both in Haulmont repositories and publicly at https://bintray.com/cuba-platform/main

To build CUBA from sources you have to build cuba-gradle-plugin first and install it to local Maven repository.

Sure. Just select a desired Platform Version when creating a new project in Studio, and binaries will be downloaded automatically from the artifact repository.