Electrical – BQ29700: Problem with the battery protection

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.

A1: The block diagram is a good start. A schematic would be even better.

A2: 5V is fine. The data sheet shows it is 97% efficient with a 5V input (see figure 7 in http://www.ti.com/lit/ds/slus534e/slus534e.pdf)