Well, I'm going to attack the infamous "amusing joke" that Sirius played on Snape sixth year in fic. I have my own ideas and will stick with them, but one I'd taken very much for granted--the timing of Sirius's running away from home in relation to the prank--seems to have the other notion equally taken for granted, and I'm racked with curiosity as to how the numbers play out.
How were Sirius's "prank" against Snape and his running away from home related chronologically and psychologically?
He ran away after the Prank; it was part of the fallout from it.
He ran away before the Prank; that was part of why he was so unstable at the time.
He ran away after the Prank; there was no relation between the two events.
He ran away before the Prank; there was no relation between the two events.
EDIT: And on the question of Sirius being sixteen during most of sixth year, JKR has been giving birthdays since late July. Sirius hasn't yet been listed, which means his birthday is between April 7 and July 30 (unless JKR is going to go back over and add names in next year). So at the very earliest, Sirius would be turning seventeen on April 7, and may well have a summer birthday the same as Harry has. In either case, he's sixteen for either most or all of sixth year.