Isolating each cell would require to use MOSFETs between cells to break connections, and usually cells are physically arranged in such a way that it is impossible for you to put MOSFETs between cells.
Why? LiPO, LiFePO4 and other lithium chemestries cells can usually deliver very high currents, we are talking anything from 20 A to 100 A or even higher currents per cell. So, they are usually connected using thick copper (or other metals) sheets.
Here is a random image I found in google showing these shunts:
Note that the ones in the picture don't look very good and that is probably a "low current" setup. Large lithium ion packs usually have much bigger shunts.
Anyways, you'd also have a lot of losses from the internal resistance of all those MOSFETs.
If you want to charge the cells, you can use a buck converter to step down rectified voltage from a transformer connected to mains. You'd have to implement a PI or PID control loop with a microcontroller to control the duty cycle based on the output current, but you'd then have to implement some kind balancing to keep the cells' voltage in check. This could be another buck converter connected to the battery that would be able to transfer small currents to each cell so that you can balance the cells that are lagging behind.
The kind of digital controll you need is not easily done with a simple arduino, nor does the arduino have the necessary kind of ADCs to allow for fast switching frequencies.
I recommend you read the book "Battery Management Systems for Large Lithium-ion Battery Packs" by Davide Andrea and the book "Fundamentals of Power Electronics" by Robert Erickson and Dragan Maksimović. These books will teach you about DC/DC converters and BMSs and give you the necessary knowledge you need to create something like you want.