Blue team Karthus 'walls of pain' and purple team Jayce 'acceleration gates' the same spot and people run through?

It would have to be the purple team running through, but yes.

Um...no. The world doesn't end. Both will be affected to the person, and whichever they go through 1st (it is impossible to put them on exactly the same spot, the game would move it slightly) will then be the number effected for the 2nd one.

Not sure if that made any sense.

It's "Don't cross the streams" not "Don't cross the walls"

if two Singed's fling each other at the exact same time?

if two Blitzcranks pull each other at the exact same time

Two malphites ult into eachother at the same time.

Two Wukongs activate their ultimates at the exact same time.

SPIN-TO-WIN BATTLE TO THE DEATH