I thought shrimp was supposed to be deveined first b'cos that's where they p***. Am I wrong?

Deveining does remove the digestive tract waste. It's up to you whether you feel the need to do it or not. It's very easy, but can be a pain if you are talking about lots of shrimp. If I can barely see it, I don't bother. If it's dark and thick, I remove it.

The nerve underneath cannot and does not need to be removed.

"Deveining" shrimp does indeed remove the digestive tract. If the shrimp hasn't eaten anything, the vein will be a thin, transparent tube. If it's been eating, the contents are bits of plant and animal debris. Not toxic, but... On large shrimp and bigger crustaceans, such as lobsters, you can follow the line of the intestine all the way to where it dips under the tail to the final point of elimination. Shrimp with full guts are more aesthetically pleasing if you devein. But try not to obsess!

(The very faint dark line on the bottom of the tail is a nerve cord. You can't "devein" that.)

Actually, deveining is optional in shrimp dishes. Haven't you ever ordered peel-and-eat shrimp? those are definitely not deveined. They're cooked in their shells. And no, they dont poop in a vein. Actually, their elimination tract in underneath not on top. If you're squeamish, that's the one you'd want to get rid of. But virtually no one does.