Another thing, if the arduino already has a cap on reset pin - I'm assuming that the arduino pro mini has one (I looked at the schematic), then I don't need to add that cap to the programmer? Or it doesn't matter if there are maybe 2 caps?
You DON'T want ANY capacitor between reset and ground! If the "arduino" has such a capacitor REMOVE IT! The capacitor is connected in SERIES between DTR and the processor reset pin. The processor should have a 10K resistor from reset to VCC. A .1uf (100nf) capacitor will provide the correct timing of the reset pulse on a 5v circuit. A 3.3 volt circuit might need a larger capacitor. The value shouldn't be critical however.