The hitboxes are very generous due to the pacing nature of the gunplay - it's more about strategy - but the shotgun centre-mass is your usual best bet against heavies. The final boss has a bunch of ammo scattered about, but one thing that could be neat is meleeing an enemy gives you ammo too. Not sure yet.
You shouldn't have been able to get out to the edge at all, the entire space is meant to be enclosed! I'll look into that - thanks for the heads up!