If the problem is that the air never gets warm, it's most likely a stuck-open thermostat. If not that, heater core may be plugged.
the heater core could be pluged or the heater control valve is stuck closed
check the fuse
You may smell coolant when the ac is running but a leak in the heater core won't cause the ac not to work.
Yes it could also cause the A/C to stop working.
if the thermostate is stuck open it wont allow the coolant to reach a certain temp. which could cause the heat to not work to well.
Possibly the Heater Motor, if the fan is not coming on at all the bearing in the motor have probably gone out.
Yes
either a fuse for dash or the light switch
could be the switch to turn it on or the heating unit itself, let an professional take a look at it
Yes. The coolant carries the engine heat to the heater core. Without coolant the heater core does not get warm.
Most common things are Thermostat or a bad heater core but could also be something blocking the door down by the heater core. I changed my Thermostat and Heater control Valve to find out a pencil fell in the defroster and prevented the door from closing. Hope this helps.
The thermostat may be stuck in the open position, so that the water is not getting hot enough.