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But, IMHO the strongest point of this $19 meter is 1uV resolution, not any of his Amp range. [...]
I totally agree with that. This meter might not be entirely practical if it is your only one due to the missing ranges (and other quirks), but it has some unique features that might complement other meters if you don't have a lot to spend. Yeah, if you already have a 7,5 digit Keysight lying around you might not be especially impressed, but now I can add a µV resolution measuring option to my "lab" for just ~US$20. I have got one on its way!
It looks however like the designers had no good idea if they wanted it to be an electrical or electronical measurement device. Its square wave output sounds interesting, but I could not think of one single way I could implement it practically in an actual circuit due to the lack of flexibility and range. Personally, I would have inserted a third shunt in the meter and I would have used the position on the knob to select it. With dedicated temperature meters available I don't really need that as an option, but one could argue in its favour.
I already own an AN8002, and I do like it in a number of respects. It has relatively high counts for a €13 meter (this one's even better) and is quite accurate and has no pots in it. I had an old Uni-T which did, and it changed over time to be out by as much as 10% (in every range) until I found the proper pot to tweak (cause there's no documentation on that).
The capacitance goes down to pF resolution and is quite fast. It is also high impendance in mV range, which can be useful for some applications. It mV range also allows for measuring current with in-circuit shunts (but you'll have to design these in, which I sometimes do), because when doing electronic work breaking the circuit open and inserting a meter with its sometimes high shunt resistances and/or long inductive leads might very well interfere. The AN8008 does have an option the AN8002 does not: manually changing ranges. I often find myself wanting to do so, but this feature lacks on the AN8002. I would have considered that a more useful feature than the present "Hold" function.
BTW with my AN8002 the diode check voltage is above the battery voltage. It puts out 3,25V while I use Ni-MH rechargable batteries that are at 2,6V (these values were measured with my unit, but might differ with other ones). It must have some kind of small charge pump in it. I must note it only delivers very low currents at this voltage, but I could light two red LEDs in series very faintly and see their forward voltage (some meters seem to put out the voltage, but just not measure it above a certain level, don't know why).