Thomas G. Marshall wrote:
Fundamental questions.

Given:

If I wire two 3V 1mA batteries in parallel, the result is 3V 2mA.

If I wire two 3V 1mA batteries in series, the result is 6V 1mA.

Batteries are not rated for current, but with current times
time, e.g. mA H for milliampere times hour.

BUT:

1. What happens if I wire the following in parallel:

3V 1mA
6V 1mA

The higher voltage battery runs down very quickly, trying to
charge the lower voltage battery. The exact process depends
on whether this causes either of the batteries to be
permanently damaged or not.

2. And similarly, the following in series:

3V 1mA
3V 2mA

If those are milliampere hour ratings, then you get a 6 volt
battery for the first milliampere hour output, then you get
a much lower voltage as the larger battery tires to reverse
charge the smaller battery with whatever load the remaining
voltage drives through the load.

Does #1 above average the voltage to 4.5V?

Almost certainly, no.

Does #2 above average the current to 1.5mA?

No.