(너) 그것 잘못 했다. (or "틀리게" 했다) (너) 그거 잘못 했어/했네. (more colloquial) If you are actually seeing the result of the wrong work/action, you could also say: (너) 그거 잘못 해 놓았네. (해: do + 놓다: leave/place) "He said that he was home": 1) 그는 집에 있다고 (말)했다. Full, formal. 2) 그는 집이라고 했다. Shorter version, like "He said he's home". 3) 걘 집이랬다. In informal speech. 걘 (<- 그 애는==그는); 집이랬다 (집 이라(고) 했다) #1 is the formal version you'd see in normal text, where as #3 is conversational speech.

Yes. 놓다 is a common word used by itself or with other verbs. In "해 놓다", it has the sense of "leave, place something somewhere ready for someone". 돈을 찾다: withdraw funds. 돈을 찾아 놓다: withdraw(or have withdrawn) funds (to make it ready for me use) 일을 망치다: ruin the work. 일을 망쳐 놓다: ruin (or have ruined) the work (emphasizes the result; state) 차를 돌리다: turn the car. 차를 돌려 놓다: turn the car (so it is ready for something) 숙제를 했다: have done the homework 숙제를 해 놓다: Have done the homework (ready to be submitted - emphasize the result) 놓다 also means release; let go. 놓아! or 놔(common, contracted form): Let go! Let me go! 새를 놔 주다 (새를 놓아 주다): Let the bird go free. And yes, 집이야 is the informal way of saying "I'm home". (Let's say friends A & B are calling another friend C on a mobile) A (to C): 어디야? Where are you? C: 집이야. I'm home. A (to B): 집이래. He says he's home. * All this is as informal and colloquial as it goes.