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internal resistance for batteries, usually you test it under different loads, and the change in voltage divided by the change in current is the battery resistance. Though it moves around a bit due to temp and state of charge, and you want to be quick in taking your measurements, and take them on the flat part of the discharge curve.

capacity, just discharge it fully and measure how many amp hours it takes to charge it fully (or charge it fully and see how many amp hour you get while discharging it fully). A bit time consuming, but that is how it is done.
 

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I was thinking you just use a decent vom (I like my hobby grade vc97+) and a cheap 100 amp shunt (you can make your own shunt too), and a couple loops of wire in a bucket of water, that draw about 50 amps a piece at 3.7v.

It is totally garage doable though, been done many times, but you have to know what you are doing. You don't want to be measuring float or recovery voltages, just load 1, note shunt and battery voltage, add load 2 in quick succession, note shunt and battery voltage, and shut it down, then sort out the shunt and battery voltages to figure out resistance.
 
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