Power = Voltage x Current 800W = 12V(Lower Car Battery Voltage) x Current Current = 66.667 Amps
1,600W = 12V x I I = 133.33 A
Put your Fuse close to the battery to protect from chassis short when you go through your firewall.
I would use 4 AWG
I have also included a video on how to install a power inverter in a car.