Can you explain the ping working system of submarines?

[WompaOne]

-How does new targeting work after ping cancellation?
-When pings hit the same target at two different points, which torpedoes target which point?
-When I ping two different ships without canceling the ping, which one does it give priority?

[Ace42]

Each ping hit replaces the previous ping hit, unless it hits the previous ping in which case it enhances it to a "double ping".

Hitting the ping-cancelling button means the subsequent torps will ignore the current ping.

You can't have pings on two different ships simultaneously.

Pings are mainly for dealing with enemy subs; for saving whiffed salvoes; or for overwhelming a target's DCP.
You generally do not want to be telegraphing your position and your attacks by spamming pings unless it is both safe and necessary.