Maybe I’m mistaken, but my understanding was that with a properly verified remote cloud access ID I could see my files in a browser window and not need an extra program installed on my Mac. The FAQ shows a page with shares listed after clicking “View Shares”, but instead I’m routed to https://www.wd2go.com/jsp/webdav.jsp?deviceType=MY_CLOUD_MIRROR
To which FAQ are you referring?
AFAIK, the My Cloud Mirror / EX2 / EX4 cannot be accessed remotely using WD2go-based shares. They require the My Cloud Desktop app. Only the My Cloud, My Book Live and My Book Live Duo support this.
The EX2 and EX4 allow for WebDAV network mounts, though – I’m not sure if the mirror allows it.
MCM can be configured for WebDAV too, to answer the last point.
Web based access without software (ie via the web portal directly) isn’t possible for the MCM - it’s something that has been asked for several times and there is a request for it running in the ideas area ( here). At least it’s the same if I’m interpretting the original request correctly.