so,
about HAM, it's fine for me, I used either hildon and maemo.org app without problems until the battery problems, and I think I'll continue (however Fap could be cool to test too)

the charging issue, I'm still stuck with it, I'm charging the batteries again and I'll see when I have all of them at 4.2V (one of them is a 4V for the moment)

I did not flash it (I planned to do so but the USB problems prevented me to do so)

nor the emmc

mass storage mode, it worked for five seconds (the phone asked what mode it should enable) and after that, it shut off.

I used three devices, two with internal charger:
a port on my PC and a 500mA charger (a bit crappy) and also the TP4056 external lithium charger.

the notification led, it's a bit random but either it stays yellow, either it blinks yellow or sometimes it lights up a tiny little bit red, that's when the phone is off. When it's on, it says "charge defect" or it get stuck and shuts off.

About the multimeter, I have one (standard 30$ model, decent but nothing fancy), I also have an almost complete electronics "lab" (but I'm not much in this kind of tiny electronic devices (I'm starting at soldering SMT simple components, that's the most advanced I can do for the moment)