a battery destroyer that gives up to "800% more life"? wtf?

Hello, op-amps are not nesecary here.  The resistors 6K/11K create > 5K impendance for the ADC.  Adding a cap there should help.

The Internal reference for a 328 / 168 is 1.1V   (0.99v in my case, read after the picture)
I did not find the correct chip to use on the circuit diagram.  I've even used the wrong battery types - but you get the idea :)

You could have avoid using a voltage divider for the ADC input.  A small value cap placed very near the ADC can compensate by the high source impedance of a series resistor (also act as low pass filter to help with noise.)  The high value series resistor can be used to protect the uC.  For charging battery, you want as high resolution from your ADC as you can and a voltage divider reduces it.

If you were to use a PNP and rearrange the circuit a bit, you could have a constant current source for charging the battery.   Instead of connecting R5 to ground, connect that side to the I/O pin.  Drive it low to enable charging.

It would look like this:  https://qph.ec.quoracdn.net/main-qimg-43fd6ff7a2d38980156db66d98aa791c?convert_to_webp=true

The LED acts as both a voltage reference for the constant current circuit and as a indicator.

Sounds reasonable, but I dont have 4 of the same PNP's to hand.  I'm just using the junk I have.

For the wires to the ADC inputs, wouldn't you want a buffer/ op-amp as a follower to ensure you won't accidentally load the circuit when trying to read the voltages? It probably won't be an issue, but it may come in handy. Gotta have that precision for something that doesn't need much, right?

Regarding the overvoltage... I know what you mean, the datasheets does not say it can not go over the Vref.  Just as long as its upto Vcc.  I quick test shows no damage (luckily).

The buffer/op-amp isn't really an overvoltage issue for the AVR/Arduino, it is just an accuracy for reading the voltage of the battery as you charge it. Though checking the input current limits for the micro wouldn't be a terrible idea, which would make either the resistor as K.C. Lee mentioned above, or the op-amp protect against that. Loading the circuit would just alter the voltage read by the ADC, which could give you incorrect results. Though what may be nice, is using the op-amp with some gain to scale the battery voltage over a wider range to get more accuracy might be something interesting to do. Like map the voltage of 1.1V to whatever voltage you want across the battery, to 0V to 5V. It isn't necessary, but might help

On the ATMega8, there is an option of using internal 2.56V reference.  So you are making use of about 60% of FS.  So essentially you are losing less than 1 bit of resolution.  You can do a bit of oversampling and decimation to recover about a bit or so in real life.  http://www.atmel.com/images/doc8003.pdf

Adding opamp to expand the scale does not improve on accuracy.  It merely improve on resolution.  The two terms are not interchangeable.

http://www.appmeas.co.uk/blog/index.php/2010/04/sensor-accuracy-and-resolution-explained/

The capacitor I suggested helps a lot on the ADC as it lowers the AC impedance and provides the charges for the switched cap ADC during sampling phase.  The placement is extremely important for good reading - needs low impedance so short and fat tracks and place the cap as close to the ADC input pins as possible - similar to decoupling.  If you don't do it properly, the reading could jump a bit.  I use that for a few of my projects.