Learn English – What does “That’s O.P.” mean

I think in this context "a rip" is simply a euphemism, a more socially acceptable version of a stronger swear word. One can, after all, give or not give:
-a damn
-a darn
-a good goddamn
-a fuck (possibly even a flying fuck)
-a shit (or two shits)
-a hoot (or even a hoot in hell)
-a tinker's damn/dam
-a pair of dingo's kidneys
or many, many other things. Many of them would probably not be said by a pastor giving a sermon! So to give the same sense, but in a less offensive manner, you can choose another word, and "a rip" happens to be one of the idiomatic choices that appears to stem from a general association of "rip" with worthlessness.

"word up" is like saying "right on" or "that's right".

A "code word" is a shared secret word which signifies something else. A code word might be used to let people know that you're part of their social group.