There is a value in the vehicle building screen about fuel consumption. Eg, for an electric engine, I believe its 3 per tick. My understanding is that it isnt currently changed by how fast you go, so hammering about at full speed is probably more fuel efficient than just crawling along. Happy to be corrected by someone more informed than me though.
Tires and the like dont change fuel efficiency other than weight, the heavier your car, the slower it is, though it doesnt seem to affect it by heaps, so unless you arent piling heaps of armor on, its not a big deal.
My plan would be to grab a normal car engine and a few alternators, take out your electric motor and put it in the trunk, install your gas motor then get a rubber hose by smashing up a fridge and some big containers, jerrycan if you can carry it, gallon jugs, biggest waterskins you can carry, etc. Loot up some fuel and then start driving to your destination, my understanding is there is no point just idling the engine to charge batts when you can just be driving for the same charge.
One trick I use if im having trouble with power for my car is carrying a small electric motor in my cargo space, it will keep the car moving, but only use 1 charge per tick. You also want pretty much your whole car covered in solar panels to keep your car running at a useful level.
You can find upgraded solar panels on solar cars on roads out in the wilds, if you have spare and high enough skills, you can pull them apart to learn the recipe (there is also a book that has it). With your car fully kitted out with them and a few spares in the cargo space, you are gold. You can also get quantum panels from lab finales, but they are super rare.