Thanks so much for your help guys.
I setup the Ecobee last night and everything went (mostly) well. The only issue was that my Y wire (for cooling, I believe) was not showing up as connected on the Ecobee, even though connected. This Y wire was also connected on my old thermostat. The heating is working perfectly fine.
The Fan Coil unit in my apartment is not a Whalen, but this:
https://engineered-comfort.com/produ...del-series-39l (Model E39 LZE). I rent in a condo that had people moving in only in December 2016, and I suspect they switch between heating and cooling depending on time of the year ( I live in Canada), so one possibility is that the cooling hasn't been centrally switched on at all.
What I'm confused about is this - is my reasoning for the Y wire issue correct or is there something wrong with the Y wire? (which means the fan coil unit has to be opened). Is it a normal practice to centrally control it this way, or is my assumption completely illogical?