Troubling Battery Behaviour

VielenDank:
Thank you Steve, this is exactly the kind of information I'm looking for. So this would mean that when the resistance is showed as 0 on the meter the batteries are in the state of rebalancing?

No it means that you can't tell anything from that reading. It is meaningless.

And from the minimal description of your powerbank thingy I can't tell anything about what it is doing. It looks like its main purpose is to provide a 5V 2.1A supply from a 3.7V battery. If it does anything else like charging and how good its charge algorithm is there's no information on.

Although it's normal for a lithium battery to recover some voltage when it has been on load and the load is removed it shouldn't ever go as high as 4.3V unless you have been overcharging it.

BTW for all practical purposes you can treat any number of Li-ion batteries connected in parallel as though they were one large battery.

Steve