I’m trying to find actual free games, but I keep getting demos included in the results.
Try with status "released"
https://itch.io/games/free/released
Remember that the status is set by each developer, so there is no guarantee that it will hide all demos and prototypes (there are always developers who don't configure the pages well), but it should hide most of them.
You can't. That information is not anyhwere to filter. Itch does not know if something is just a demo or a chapter 1. And there is no free "full" game filter information either.
Even if developers would be inlined and able to accuratly give that information, they can't. A demo version can be "released" or "in development" just as well. Especially chapter 1 stuff would rather be released. And the other way round, just because something is "in development" does not mean it is unfinished.
There is https://itch.io/games/has-demo but this is for paid games that have a demo version. Itch has no concept of a whole project being a demo.