output frequency

Other Hardware 3rd Party Boards
1

Hi
arduino pro mini has 16MHz of processing frequency, but
what is its output frequency?

2

You have to be more specific. Do you wish to know the maximum speed a pin can be toggled or the frequency of the PWM pins? You could be asking about the fastest baud rate that can be achieved.

3

shortest time output between each pin

4

shortest time output between each pin? what are you trying to ask?

if you are asking how long it takes for the microcontroller to complete a given instruction, you will have to look at the Atmel's 8-bit AVR instruction set. Some instructions may take just one cycle, some take more.

1 cycle = 1/16000000 Hz = 0.0000000625 seconds = 62.5 nanoseconds

You can set the output for the PWM pins. I'm confused as well as to what you're asking but this might answer your question?