Non-isolated Off-line AC to DC Power Supply
On bottom schematic, the zener diode is a protection device for the gate of the MOSFET, perhaps to keep it below 15V during power on transient.

The 220pF is really small for 50Hz/60Hz, so it is probably not for conditions under normal operation. Perhaps it is for the same purpose as above. In that case, the zener diode is more solid.

The period that current flows from the input to the capacitor occurs during the peak of the triangular spike. If that period is only 1/20 (a wild guess) of the total time, the corresponding current pulse would be 20x100mA=2A. Something like that is going to stress all the components along the power path. That includes the diodes, the MOSFET and the 470uF capacitors. Don't expect the capacitor to have a long life even at 100mA average.

The other limits is the output ripple voltage with the 470uF. That is easy to calculate 0.1A / (470uF x 50Hz x 2) = 2V.

If you trust the original design decisions, then to get 200mA you can try to increase the current ratings of the diodes and MOSFET to 2x, and the 470uF to 1000uF.

By the way, I assume you understand the safety aspects of working directly with main AC. Personally, I would not use a circuit like this when proper isolated designs and modules are quite cheap already and easy to come by.