Check for a fuse, circuit breaker, or a self resetting circuit breaker between the batteries and the fuse panel in the second picture. If it tripped/blown, it is likely there will be no pump, lights, or fridge. Slide and jacks work because they will be direct connected to the batteries due to their high draw. All 12V works when plugged in because converter is providing the power it just may not be getting to the batteries. So, measure voltage across the thick red and white wires in the second picture and across the +ve and -ve of the batteries when plugged in. They should be the same and at least 13.3VDC. If less, there may be converter issues.
Electric space heaters and the AC are 120V appliances. If too many are used or additional extension cords are added to the shore line, the voltage in the circuit will drop resulting in low power and possible equipment damage. I'm surprised you could run more than one 1500W heater without tripping the breaker at the pedestal which makes me think the inverter or load sharing was somehow in play. If the inverter was in play, the converter was trying to keep up delivering 12V to the batteries which could have tripped/blown the above mentioned 12V safety devices. If the converter was trying to keep up while multiple space heaters were running, the 120V system was surely overloaded and voltage low.
Check for fuse/breaker/self resetting breaker in 12V cables.
Verify at least 105V in the AC circuit when running things like heaters and the A/C or equipment may be damaged.
Verify voltage out of the converter and at the batteries is the same and more than 13.3V.
Worry about the inverter later.