Battery Project

I am new to Arduino world, but I think I am learning fast.
I have already built a programmatic able timer to control multiple heat lamps for a bearded lizard.
My next project is an automatic 18650 charger/capacity tester.
I am using an Arduino Nano as core.
I have already worked out programming to check capacity and recharge the battery but i need 6 pins for each battery.
1 for temp
2 for battery voltages.
1 to turn on mosfet to turn on/off TP4056.
1 to read when TP4056 as finished charging.
1 to turn on mosfet for dis-charge curcuit.

I am investigating the MUX74HC4067 to multiply my input/output pins, but what i am finding is when you change channels on the MUX it cuts power to last channel that was used. So i cannot use the MUX to drive the mosfets to turn on.
Example: I turn on mosfet to discharge the battery, I need to sample the temp and battery voltages. When i switch channels to check them, the mosfet turns off.

Also during my MUX74HC4067testing, I built the simple led scroll and noticed that on several channels multiple leds would light up when switching channels before settling on correct channel/led. Any thoughts as to why. This was an example sketch.

In order to increase inputs or outputs of Arduino, I have always used shift registers, two I normally work on are 74HC595 & 74HC165, one is used to increase input pins and the other one is used to increase output pins.

I purchased a sleeve of those. Can you have multiple channels on at once?