Dave Plowman wrote:

[snip stuff that doesn't like the problem]

Can every PC ping every other PC regardless of what they're connected
to, by IP addr? by name?

No. Only when they are are all cabled or on the same Wi-Fi

So you've got a network issue, not a file sharing issue.

Does the range extender plug into an ethernet port on the router, or is
it purely a wifi device?

Does the extender use the same wifi SSID as the router?

Does the extender have a web management interface?