Assuming the hella is 24v and its a 15 amp plug which is the highest I’ve seen so far, then the max it can take is 360 watts. For safety let’s say 300w max usage.
If it was 12v then it would be 180 watts max, so maybe 150 watts to be safe. 800w inverter should be fine as it wont actually pull that…unless they connect a 64" 3D curved TV. 
As for cable, yeah should be alright but would use the thickest that will fit.
Edit: what Andrew said.