I've inspected my own HTTPS traffic a number of times using it including e.g. traffic from e.g. iPads where my Desktop was effectively acting as "the edge device". Of course, this is more for debugging than aggregate statistics/monitoring...
This won't let you inspect traffic secured via certificate pinning without additional reverse engineering to figure out how to replace the pinned cert, but it'll work fine for vanilla HTTPS / generic CA based stuff (e.g. all browser traffic.)
Replacing a cert doesn't get around cert pinning. That is the exact use case that cert pinning protects against.
For public certs: Yes, but that would only produce the desired effect if the site hadn't yet been pinned, and this was a first connection, or in the case of the pins having expired. In other words, the pinning can only be stripped out if there is no pinning already in place on the client.
However, this will soon be a moot point, as Chrome removes pinning in favor of cert transparency. This will reopen this security hole in browsers simply trying to be secure within captive portals and other insecure networks. Tor has pinning that would extend from inside the portal to outside, so that may be one option, but I don't yet know how sturdy that is.