They are not interchangeable with "pay it forward". "Pass it on" and "pass it down" generically mean to give something to someone else. For example, you learn that class is cancelled and want me to inform others, you would say "class is cancelled, pass it (the message) on". Or if I'm giving a presentation and want to distribute a stack of copies, I would give the stack to the nearest person and say "take one (copy) and pass it (the stack) down."
"Pay it forward" is a more specific saying that means instead of returning a debt/favor, give the equivalent to someone else instead. This debt/favor is not implied in "pass it down/on".
Now, a related saying is "take a penny, leave a penny" but this is specifically for a store change tray where one might leave unwanted change in case another customer is just short in cash by a few cents in expectation that if another time the one just short is you, that someone has left some change as well.