Using supercapacitor as backup for MCU

I have this project that requires some kind of backup power supply. and I am planning to use a 5V 4F super cap.

there are my questions:

  1. I am planning to charge the cap with a diode and 100 ohm resistor to a 5V VCC (Good idea?). how can I connect the cap to the MCU. direct connection will not work because it will take some time for the cap to charge up.

  2. Normally the circuit will consume 20mA, in power-off mode, it will use about 200uA, how long will this 4F cap last?

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