How to choose a battery charger?
For example, a dry battery is nominally 1.5v, which can make a small light bulb turn on and turn a small motor, but it is impossible for you to want it to light up the lights in your home. If you have a voltmeter, you will find that when it lights up the light bulb, the voltage is still almost 1.5v, and when the small motor is turned, its voltage is much lower, and when you connect it to your home lamp, its voltage is almost the same is zero.
That is to say, when the output capacity of your adapter is less than 1.5a, the voltage is basically within the allowable range of the nominal voltage. It is to convert the AC power supply into a DC power supply with a 7.2v output current less than 1.5a.
How to charge is determined by the circuit on the charging board. The size of the charging current and the cut-off voltage are determined by the circuit on the charging board. Generally speaking, the voltage of the power supply you add to the charging board is higher than the nominal voltage of the battery. As for how high it is, it depends on the tolerance of the charging board. If it is a charger specially used for charging various batteries, its withstand voltage is generally very wide. High 5v, 8v, and some dozens of volts are fine. If it is a dedicated supporting charging board, such as on a mobile phone or a notebook. Then their withstand voltage range will not be wide.
From your description of charging, your understanding of electricity is not enough. You think the power supply voltage is constant, you want to drop some voltage by connecting a diode and a small resistor? Your modification is wrong. Lithium batteries are extremely sensitive to overcharge and overdischarge. Without understanding the circuit, random modification will only make your battery stop quickly.
In order to prevent reverse connection, it is ok to add a diode, but the battery capacity must be lower.
By the way, q1 and q2 are two protection tubes for long-term pressure on the battery. They are usually connected. Only when the battery voltage is too low, it will open the circuit and stop your power consumption, thereby protecting the battery. This short circuit is fine, that is, the protection function of the battery has failed.
And the part of the circuit outside your red line is the regulated output circuit, which means that the voltage of your battery keeps dropping and the voltage of vout is kept stable and constant when you use the battery.
The problem you mentioned is mainly because of the fear of short circuit and sparks. The easiest is to add an enclosed fuse. Either add an overcurrent protection circuit, but this makes it more complicated.