Electronic – How do we get the proper USB charger for tablets with varying cable lengths and gauges

It's not too hard to design, as a computer controlled switchmode power supply. But it will be more expensive than just buying one of each kind of charger, and if you want to deliver 15V @10A (for charging the car battery) it will be quite bulky.

The key issue is that switchmode devices control output power by varying the pulse width. If you have 100% duty cycle corresponding to 150W (for the car battery) then the <1W for the AAA battery will be <1% duty cycle: a series of very narrow pulses widely spaced. That's bad for precision.

Then there's the safety issue. If you configure it for 12V @ 10A and plug it into the 1.2V AAA battery you'll have a nasty fire on your hands.

Charging just 3.6V (phone, 18650 cells) and Nicad/NiMH is a more reasonable prospect. Don't forget to build battery simulators for the three types before testing with actual batteries, so the inevitable bug in the design doesn't do damage.

Amperage does not work the way that you are describing.

Basically, a power supply puts out a specific voltage, and then the device draws whatever amperage it is designed to draw (assuming the power supply can put out enough voltage). If a device takes 1 amp at 5 volts, you can use any 5 volt power supply as long as it supplies at least 1 amp of current.

My guess is that the 1 amp power supply is not powerful enough for the tablet to detect - it's likely that the voltage is sagging down below the voltage that the tablet needs. If that is true, then you can't charge the tablet with the 1 amp power supply.

You cannot hook two power supplies in parallel and get the sum of their outputs.

I would look to power the tablet directly from the battery with a power supply that puts out enough to drive it directly, and then come up with another way of detecting whether the car is running.

I would look