12V amps
At 12 volts, amps are watts divided by twelve. A 60 W load pulls 5 A; a 500 W inverter load pulls 41.7 A. Twelve volts is why vehicle and van wiring is so much thicker than mains wiring for the same power.
How to work out 12 V current
Twelve-volt systems punish inefficiency twice. The current for a given power is nearly twenty times what the same load would draw at 230 V, so cable has to be far thicker; and because voltage drop is a percentage of only twelve volts, even a small absolute loss is a big proportional one. A 0.5 V drop is 4% at 12 V but 0.2% at 230 V. That is why serious van and boat installations move to 24 V or run high-power appliances on their own short, heavy feeds.
Questions
8.33 A. At 24 V the same load is 4.17 A, and at 230 V just 0.43 A.
Above the running current with margin. The 125% row is a starting point, then round up to a standard fuse size.
As close to the battery as practical. The fuse protects the cable, and unprotected cable between the battery and the fuse is the dangerous part.
Because current is high for the power. Thick cable also keeps voltage drop small, which matters far more at 12 V than at mains voltage.
It will not shock you, but a car battery can deliver hundreds of amps into a short and start a fire in seconds. Fusing is not optional.