If you switch off the charger and then immediately (like a millisecond) read the battery voltage then you will get the charging voltage. The surface charge will take some time (and some current) to dissipate and give the true battery voltage.
I would try to measure the current while charging and don't switch the charger off. The LTC4054 could have problems if you switch it off and on rapidly.
Those LTC4054 is supposed to be connected directly to the Li-ion cell. I don't know what the mosfet in between will do. Can you use four LTC4054 ? They are 2 dollars each ?
To measure a voltage, connect the battery (+) via 1k protection resistor to Arduino A0.Perhaps you need a good voltage reference for the Arduino for precise voltage measurement.I don't undestand the 10k, p-channel and 220k. The 220k can be 1k to the gate. The p-channel should change source and drain.
You should be reading the cell voltage under charge in order to protect it - oncethe LTC chip has entered the trickle-charge regime the difference in voltage you'llsee by disconnecting the charger will be absolutely tiny as these cells have extremelylow internal resistance.So don't bother switching the charger at all.If you want to multplex reading several cells then an analog switch chip is simpler than using separate MOSFETs.