Can the Schluter-DITRA-HEAT-E-RS1 thermostat be installed to replace an existing Schluter Thermostat? Can it be installed to replace a non-Schluter Thermostat? How is it installed?

Yes, the thermostat can be used with any electric radiant floor heating system. Consult with a local electrician to ensure electrical specifications are met. There is no additional hardware required than a Wi-Fi signal and a router with good connectivity. The same line and load principles exist.