Electrical – How to charge a lithium-ion battery from a solar cell

1] VOLTAGE: 3.6V or 3.7V - 18650 Li Ion Batteries

All single cell lithium ion batteries are going to be 3.6-3.7v. There are applications where multiple cells will be tied together in series. This will result in voltages that are multiples of 3.6-3.7v. So as long as you match the number of cells and approximate mAH you should be fine.

2] Possible Voltage Shortage?

The voltages and battery life responses for all batteries are going to have slight difference. For the most part this won't matter. Most projects that use batteries are not terribly voltage dependent. They will either boost or regulate their voltage to get the voltage they want out, or they will be able to run at a wide range.

As a note, "Shortage" in this context usually means you are creating a short across your battery. Might want to be careful with that terminology.

3] Fundamental Reason for this Voltage Range

I am not an expert on this, but I know it deals with the chemistry of the battery itself.

4] Parallel Cell Charging - One BIG Li-Ion Battery Pack

This can be done. There are some issues that can come up when doing it. This might be worthy of a question by itself. If you do ask, might want to ask if the same can be done for packs in series.

5] Charging... How?

Same as previous answer.

The in-battery protection circuitry is usually intended to act as a gross fault protector and it is strongly recommended that it not be relied on as a means of charging control. As a means of gross short circuit protection it may be suitable as long as the values they choose for max Iout are acceptable to you.

For charging, use of one of the large number of LiIon charger ICs is recommended.
A major factor is that the over voltage circuit does not remove the applied voltage when the CC charging current falls to a low value. This means that the battery is "floated" indefinitely with the risk (I'm told) of plating out metallic Lithium.

A PV panel (solar panel) that is nominally 12V rated and intended for charging lead acid batteries, will have a loaded Vout of about 18V and an O/C or light load Vout of over 20V. The maximum voltage that you need AT the battery pack is 4.2V/cell or 12.6V in your case. PV panel available Iout values are a reasonable approximation to being linearly related to isolation (sunlight level).

However, Vout is not related to light level in the same way. A PV panel will produce over 90% of its full power voltage for light levels of a few % of maximum and above - say at 10%+ to be safe. If you want the panel to charge the battery to fully-charged even on a low sun day, if necessary, then you need a panel that is full load rated at at least 12.6V/90% = >= 14V. As above, as an SLA targeted 12V panel makes about 18V at full-sun full-load, such a panel will provide more than enough voltage under all practical light conditions.

You will get substantially longer cycle life from a LiIon cell if you terminate discharge at a slightly higher voltage than allowable absolute maximum. With LiIon , below about 3V under medium loads you have used the large majority of the stored energy.In-battery low voltage cutoff circuitry will probably allow discharge to about 2.6V/cell, which is lower than is wise for good battery lifetime.