Can PWAs operate with local data? Can they interact with data from anywhere in the file system?

yes, with the File System API, it needs user permission though (which is a good thing).

	▲	famouswaffles 36 minutes ago \| parent [-]
		Permissions are fine, but on android they happen every single time for the same file (and there's yet no option for the 'Allow everytine' that is present on desktop chrome). This is pretty horrible UX for some use cases.