I think there should be a notification for every time a person posted on your thread/every time a person quoted you. Because i sometimes got lost on what thread did i posted on

You can subscribe to a thread if you want to be notified[and I believe it notifies you on email as well].
It's under the Thread Tools.

I kind of like the idea of just having like a little notifications tab just for convenience.
Though I could see why someone would make the argument that it's not really needed.

There is already a "tab", it's in the usercp. Do you mean a different sort of tab?

Ya, like just a tab next to or under pms or whatever, with like a little number next to it to show the number of notifications.
I think that would be convenient