Can I change the default folder that draw.io saves its' xml files, and and downloaded image files, to? At the moment they keep going to my Downloads folder which doesn't work for me.
It depends, see below. Some browsers don't provide the permissions to perform a folder selection when downloading a file, browsers are very restrictive about file system access.
For these browsers, the only option here is to change the download folder in the browser options while using draw.
If you use Chrome 83 or later draw.io supports Native File API, which will open your operating system save dialog, allowing you to save anywhere.