But why wouldn’t they keep looking for the Best Pilot in the Resistance and the traitor that knows about their entirely secret Starkiller Base? I think a squad of 8-14 soldiers in TIEs and perhaps a shuttle would find both people quite handily, especially since life detection equipment was in use in ANH and ESB by the Rebellion and Empire.
They probably assumed, like Finn, that Poe died in the crash. As for Finn, I’m not sure how your suggestion fixes this? I don’t know how to explain why they didn’t find him earlier than they did.
Since Poe says he was thrown from the crash, it makes it sound like he didn’t eject.
It’s a little ambiguous, but it’s a lot easier to assume he meant he ejected than it is to assume he meant “I heard troopers and thought you were captured” when he said he didn’t see Finn or a ship. Not to mention, if Poe woke up before Finn, why didn’t he make it to the town first?