#1 Are the remote relays wirelessly controlled by the main T-Stat or does it require low volt cable for control?
The thermostat and relays are both line voltage and wired.
#2 Can it be used with an inductive load? I/e a fan
Yes, this thermostat can be used with fan heaters.
#3 Is there any way for this thermostat to cool or go down? The current unit in my apartment won’t go below 70 degrees no matter what I do!
This thermostat has a temperature control range of 41-95°F and should be able to go down as low as 41°F. We will need a little more information from you to assess this.