Electrical – 18650 in series while charging using TP4056 and connecting two buck regulators LM2596 in parallel, is it safe

1. I don't think this is by definition a wasted exercise to your developing interest in battery technologies. I do think there are better ways. There are charger ICs on the market for nearly any number of cells in series. But, if it's for testing your idea, this should be fine.

2. Yes, but they will regardless of how you charge, discharge or store them. Just if you let them discharge below a certain level or charge over another level, they will degrade much faster. With an intelligent charger system, which I think your PCBs are, overcharging should be protected.

3. In charging: No, in fact, they all get charged to full. In discharging yes. This can cause increased deterioration, which then makes them get out of balance faster, which causes a snowball effect. How can you prevent that? When they are in use, make sure they are protected from over-discharge. By this mean, each cell individually. Just checking if the total gets below 7V or 8V is not going to help, you need to have something that protects each cell from going below 2.5V. Here I note that some of these charge managers I mentioned also do this for you; they are a complete battery pack protection solution.

4. You will need a set of isolated DC-DC converters. Which types are the cheapest depends on how and where you get them and where you are having them delivered, but many different manufacturers make DC-DC converters with 5V output at 100mA to over 20A. Just make sure they are fully isolated.

Batteries are tricky nonlinear devices. If you want to build a safe and reliable lithium battery charger, you need to know more about your batteries and your battery charger circuit. In general, lithium batteries are not interchangeable and not all chargers will work with all batteries.

There are also significant differences between lithium (probably not what you mean), lithium ion (probably what you mean, sometimes written Li+ or Li-ion), and lithium polymer (sometimes written LiPo) batteries, and significant differences within the battery chemistries of these categories.

The datasheet I found for TP4056 does not say that this device includes undervoltage protection. It only provides charging. Perhaps other circuitry does on that evaluation board does. The appropriate discharge protection is a function of battery chemistry, and the threshold should set according to the battery manufacturer's datasheet (as a baseline, anyway).

A circuit that tests for undervoltage is probably measuring the battery under load, and will need to compensate for the battery's internal resistance \$R_{internal}\$ reducing the voltage at the terminals \$V_t\$. That is

$$ V_t = V_{oc} - IR_{internal} $$

So to answer your second question it's quite possible that \$V_t\$ = 2.5V is an appropriate cutoff for a battery with \$V_{oc(min)}\$ = 3.0V, if \$ IR_{internal} \$ ~ 0.5V.