When Zorro is demo/live-trading for a period of, let's say, 15 min? Or let's say even longer for a period of a few hours? Is Zorro able to recover by itself? (E.g. such as Interactive Brokers platform which does that without user intervention)

Reason why I'm asking is that my area has occasionally spotty and laggy internet connectivity (my family is also all on the same network).

Loss of internet connection is a usual and frequent problem. In such a case Zorro attempts to re-login in regular intervals until the connection is established again, then continues trading.

Also if your running a live demo and a new version of Zorro comes out, can you install the new version while continuing to trade? Or do you have to stop trades & close Zorro to upgrade to a new version.

You can not install a program while it's running. But you can normally stop the old Zorro, install the program, then continue the old trades with the new Zorro. This would not work when the trade format has changed, but that was not the case in the last updates.