I agree that you can run the water pump without being plugged in. It might run slightly slower, because it is running on 12.5 volt battery power, not 13.2 volt converter power.
The 15 - 20 amp power supply will provide 120 volt power to the converter, and only 3 amps of 120 volt power will provide 30 amps of 12 volt DC power. So the electric cord is not going to need to use much power at all.
Even running the 6 amp DC furnace is not a problem, it will only add about 0.6 amps to the 120 volt power cord.
The 12.5 amp air conditioner, and you might need to upgrade to a large extension cord, as that is a lot of power. In addition to the A/C, the converter will stay on (unless you unplug it, or the battery is already full).
Good luck!
Fred.
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