Funny enough, casting tapes indicate that Leia was originally supposed to give a reason why they would head to Yavin anyway, but it was likely cut for pacing reasons.
As for the escape pod, while the line, “It must’ve short-circuited,” implies otherwise, it’s entirely possible that at least one of them might’ve thought it was a decoy, and thus wouldn’t be able to have their guns in position to fire at a pod that did contain life in time.