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the Advanced DC should work, the smaller pancake motor would be ok for a motorcycle or scooter, it would be great for a bicycle, but not a good fit for a car.
the 105amp hour battery you linked to is a bit small, a 6v battery of the same physical size would give you twice the amp hours and hold up better, giving you more miles per dollar spent.
The charger is going to be a bit slow, like 25 hours or more to charge your car, you are going to want to look at suggested charge rates for the batteries you use, but I would say a 10 to 15 amp charger is going to be better, basically as high of a rate as your power source can handle.
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