Files are a special case, and there are already plans on reworking them so maybe in the future they won’t only be downloaded on-demand. Please vote for this if you would like something like this.
Yes, files are currently just copied into Anytype and are separate.
This question and answer is not about the export. It’s about your local data that is always there even without exporting first (and again, the files are the exception here atm).
For exporting, I would guess that it does indeed export all files (including the ones which are not currently stored locally). You would obviously need internet connection for this to happen since it will need to download the files first. I’ll check with the team what exactly happens here.