The fridge draws 5.1 amps, but based on outside temperature and how many times the door is opened the duty cycle (how much time its ON versus OFF). Typically I have observed between 16-30 Ah draw in 24h period, hence they say they draw is 0.7 to 2.5 Ah (16.8/24 or 60/24).
But regarding wire gauge, 10 gauge should be minimum considering the 5.1A current and the distance between battery to the fridge.
One other thing you may want to check is the alternator load. In one of my trials, I tried to boost voltage (used voltage doubler) to increase my secondary battery charging rate (I have dual battery LiFePO4 setup). Turns out, I cannot draw more than 15Amp for charging from the alternator as the alternator is near its rated capacity.
The charging rate I have observed is around 0 to 15amperes, based on electrical load used in the car and my dual batter state of charge (takes less current when near full).
Lastly the draw of 0.75 amps when using 110v outlet is mostly because of the inverter rating limit and not the fridge. Its converting DC to AC and then again AC to DC , so cannot be efficient compared to DC to DC use.
