Converting two-wire thermostat to three-wire if you have extra conductor [easy - no adapter]

[speadie]

you might have a system that expects a dry contact. you need an isolation relay for that.
my diagram for dry contacts and similar is here:

Wyze thermostat simplified block diagrams

The wyze gets it’s own power from Rc and C, so technically, if you connected one of the normally switched lines to C, there might be enough juice to power the wyze and the other load, although putting them in series like that might drop the voltage to the point where it doesn’t work quite right. Normally the loads are in parallel, to minimize voltage drop. For your second question, the wyze has internal circuitry that detects if something is connected to Rh and switches the heating loads to it …