TL;DR: Go to the bulleted list below.
As a weekend project I tried to design a simple power supply (without sofisticated switching mode ICs, since they are very hard to find where I live). So after some calculation and study, I came up with the following circuit, it is supposed to be a 7V 4A power supply for small projects, enough to power some microncontrollers (5/3.3V 100mA), small DC motors (5V 1A), and charge a li-ion battery :
I am aware of the nonidealities of these components, so extreme precision is not a important role here, since I don't intend to replace my good ol' bench supply. I will wire a digital voltmeter/ammeter to the output for calibration.
That said, I would like to ask some questions:
About the resistors R3 and R6, is it correct to pull up a MOSFET gate for such operations? Should I pull it down instead? Or remove the resistors? I am concerned about LM324 output sink/source capabilities with those resistors.
Also, in my output circuit, should I add other components to improve safety and stability?
And last but not least: is it safe to charge a li-ion battery with this circuit? (Considering a 2200mAh battery, with 4.2V max voltage) If not, how could I improve this circuit to achieve this?
Any help/advice will be very apprecieated!