How long are the default times for greylisting with postgrey? [closed]

In postgrey when receiving email the default is 300 seconds. That is, if the sender retries within 300 seconds it will be rejected again. Change that to, say, 60 seconds in /etc/default/postgrey with

--delay=60

It's entirely dependent on the software being used to perform the greylisting and almost all of them will have a method to customize this value.

edit after your edit to the question:
Speeding up email traffic to partners using greylisting would involve getting your partners to exclude your emails so they are not delayed by the greylisting process.

Speeding up receving emails someone sends to your server will be hit or miss because different sending MTA's will retry at different intervals. If their first email is greylisted, the sending MTA might try to resend the message after 5 minutes, or 30 minutes, or sometimes never (it depends on how they have their server configured). You can "speed it up" by not using greylisting or whitelisting specific sender domains on your end to not deny the initial message.

I assume you're the sending party since you've then mentioned the receiving party.

The delays on the sending party's side (you) is entirely dependant on the software being used (you haven't mentioned). In Postfix, there are various configuration parameters to control this, the default retry timeout being 300sec (5 minutes) in current versions.

As for the delays on the receiving side (the ones enforcing grey-listing), there is no technical method to determine their configuration. You either need to reach out to the admin and ask politely, or do a series of trial-and-error tests. If I were the remote admin, I'd much prefer you ask me first.