The Shadow King entity got got for what may have been the first time in their history together which may well have actually separated him from it for the first time since he was a child.
Shadow king has been killed a LOT. The last time was pretty definitive, but you know how comics are, especially with weird supernatural entities like whatever SK is.
He's residing on Krakoa and not in a black habitat, so there's no way the council wouldn't know he's there between Krakoa itself and Black Tom.
he's not residing anywhere. Shadow King is an astral entity that possesses other people, and given the strength of it (he was traditionally as strong as Xavier, and the last appearance in Astonishing Xmen he was stronger than Xavier) staying undetected isn't a problem especially if no one is looking for him.
DNA has a half life of 521 years, so Sinister would have no problem getting his hands on Farouk's DNA if he wanted it and could find his corpse. Which, I mean, it's Sinister. He isn't going to have trouble finding a corpse.
The usefulness of DNA depends on the conditions of the body. If perfectly preserved, you can have useable samples that last hundreds or thousands of years. For a dead corpse left to rot out in the sun, you're looking at days to weeks. Farouk was a random crime lord in north africa when Xavier killed him. Even if anyone knew where to find that body decades after he was killed, it wouldn't be in any useable condition.
The big question is whether or not Xavier had the Cerebro protocols up and running before the last time Farouk died.
Xavier wouldn't have been able to "back up" Farouk's mind against his will, because Farouk was the stronger telepath AND had no motivation to cooperate with Xavier.