In the power supply design, Q1 should be replaced by a Diode. The current circuit works just because of the internal reverse diode of the transistor. The replacement is recommended, because current forward voltage of Q1's inverse diode has 1V forward voltage and it will dissipate power from the cell. It could be changed for a diode like D2 with the anode connected to where the drain is currently connected, and the cathode connected where the source of Q1 is connected. Other possibility for the diode would be the "CDBA120L" or "DFLS130L".