Maybe Darood was really Arab but he never had childeren like that. It could be that todays Darood just carry his name because he was their teacher. Only Allah knows.
J1 is older than Qathan and Adnan. I think Adnan are mostly under J1 FGC11 while Qathan being much older is difficult to tell. It is believed that the tribe that Nabi Ibrahim belonged to that settled Iraq

were originally from Arabia because FGC11 seems to have origin in southern Arabia because this lineage has high diversity in southern Arabia. This makes perfect sense because Semitic nomads always invaded the Fertile Crescent starting with Akkadians, followed by Amorites, then Aramean then Ghassanids & Lakhmids etc all