I have a similar "drill" though from your description some details are different on mine.
Mine is made very similar to a standard ratcheting pipe threading set (only smaller and much more precise). Plus I've got two holders. One has the tapered square you describe (however I've not got any bits) but the other is a #2 morse taper. On mine the jack screw is knurled for hand use instead of hex.
Use would be very similar to the way my air drills work. For a example of that see the following.
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