2000
Yes you can.
Current (amps)=Watts/Volts =2000/120 =16.75 =16.75 amps
The BTU is an Imperial unit of measurement for energy. The watt is the SI unit for power. The BTU and watt measures different quantities, so there are no 'BTUs per kilowatt'!
One joule per second equates to:One watt or,0.00134 electric horsepower or,3.412 BTUs per hour.
It depends on the source of DC that is powering the inverter. Since the inverter is 2000 watts, that just means it will handle your 1500 watt application. At 120 VAC you are drawing a little over 12 Amps. If this is an inverter plugged into a car it will run until the battery runs down, whose time will be lengthened if you keep the car running. Your battery will have an Ampere per Hour rating. If for example you had a 50 AHr battery it could supply 50 Amps for an Hour so your heater would run for about 4 hours.