WiGLE.net

As I'm a noob to this, despite appearances, I'm not deliberately trying to be stupid but . . . .

On the map, it is possible to zoom in on a particular SSID and get more info on it such as whether it supports WPS?

If I can't get that info by zooming in, then how else can I get it - without going to that physical address in person?

you can click (as a logged in user), or you can use the Basic and Advanced search functionality to get al the information regarding the point.
WPS will be listed in the capabilities, which aren't part of the site rendering - check out the API for more details.