Electronic – Batteries connected both in series and in parallel

Current will flow between the batteries based on the difference in terminal voltages, not based on the difference in State Of Charge (SOC), and certainly not based on absolute capacity (equal mAh remaining). The terminal voltage vs. SOC curve is highly dependent on the chemistry and manufacturer of the cell, so don't assume that two cells will behave the same even if they have the same nominal voltage. A typical voltage vs. SOC curve for a Lithium ion Polymer cell looks like this:

In short, while you might succeed in moving a little charge from a full cell to an empty cell, current will most likely stop flowing between the cells well before they have equalized SOC, and they'll never end up a the same amount of stored energy remaining given that they're different sizes.

If you want to use one battery to charge another battery, consider a boost regulator in conjunction with a charge management IC. In your application, you would use a boost regulator to get to 5V from your external battery, then use your normal USB charger to leverage the existing charge control circuitry for you phone. You won't even void your warranty!

This is either dangerous, not advisable or doable depending on...

It comes down to what the "cells" are made up of. Since a bare single cell doesn't have a TH, you are talking about a pack. It may be a pack of 1 single 3.7V cell, in which case it's effectively a cell and you can, to a limit, connect in parallel to your heart's content.

I'd advise you to balance them out to each other with an extra resistance before you hard connect them, though. If they're large cells and 0.5V apart that will mean large currents will flow until they "agree", which is good for neither the low one, nor the high one. It would look a bit like this:

^{simulate this circuit – Schematic created using CircuitLab}

You should pick a TH contact, since it is a temperature sensitive resistance that will be measured, if you connect multiple in parallel it will measure a low resistance, compared to what's expected. Since usually they are NTC 10k, that means the charger will think your batteries are hot when you first connect them, which means it will not charge.

If you have a pack of more than 3.7V, such as 7.2V or 11.1V, then connecting multiple in parallel without any "internal cross connections" will increase the speed at which the first cell will die. If the pack is multiple cells in series without any balancing connections, it can be debated whether that's advisable to start with. But anyway.

If you have a 2 cell in series pack, you will want to connect them like this:

^{simulate this circuit}

This way the odd batteries will join force as will the even batteries and that will severely decrease the statistical chance of a dangerous defect in the pack.

((Of course it's better to start out with resistors for the parallel connections for the first hours to cross-balance again))

If you have a multi cell pack and can't make the cross connections as drawn above, I'd say, on balance, you're better off not connecting anything in parallel at all. Especially for charging purposes.