Does this look okay?

I’m making a parallel/series switcher for two lithium ion cells because I can only charge them in parallel, but my project requires 7.5v. I’m using NPN transistors as switches, controlled by Arduino to switch between charging and discharging. The analog pins are used because all of the other pins on my Arduino are being used by a motor shield. The analog pins would be set to output.

During charging Q1 and Q2 would be saturated, and Q3 would be cut off. Vice versa for discharging.

Also- Ignore the connection between R1 and battery negative, imagine R1 is going to Arduino ground instead.

No that would not work.
The batteries appere to be floating but it is so badly drawn it is hard to tell.

Of course in practice it would be connected to a load.

You have to show the load and how this is referanced to the ground of the arduino because your base voltages are referenced to that.

Hows this?

I don't think you get how transistors work. To turn on a transistor the base must be higher than the emitter by at least 0.7V. If you power your arduino from the resulting voltage it will only be getting one battery's worth of voltage in the so called parallel mode. When switched to seriese the output of the outputs is at most 5V and will not control the transistor.

Basically I think what you are trying to do is impossible and also unwise. Are you sure you can charge batteries in parallel? What makes them shair the charging current evenly?

Lithium batteries self equalize when charging in parallel. However I do now see that transistors are a no go. Relays should be fine though right?

EDIT: Wait would it not work in reverse active mode if the emitter(8.4v) is larger than the base(5v) which is larger than the collector(0v)?

You might also want to read the thing about "how to use this forum". The part about writing a useful title in particular...

Relays should be fine though right?

Yes except when they are in the parallel mode you will effectively pull the rug from your arduino leaving it short of voltage. I don't know what you are trying to do with your project but I would suggest looking at using only one battery and a DC to DC converter to get you to 5V or what ever voltage you want.