Attacking the enemy from the side or from behind increases the damage dealt and nets you a bit of extra experience.
Experience is earned by way of "gems" dropped by each mob killed. Gems will follow the adventurer, items will not. It is possible for gems to get caught on obstacles and not make their way to the player; if they leave the screen, they are lost. This happens just often enough to be distantly amusing, not enough to significantly impact xp gain.
Recettear uses sprite mirroring. All adventurers are right-handed unless they are facing east.
Enemies that are off screen exist in a state of suspended animation--all attributes are frozen. If you run out of the screen just as a statue is firing rings at you and he gets two off, the remaining two will be fired as soon as you re-enter his space and "awaken" him.
Ropers are an exception to this rule, and can see and approach you from one room away.
"Ring around the Rosie" Blue Slimes are another exception, and you can see them continue to sing and dance on your minimap. It therefore seems likely that Formation Gnolls are similarly excepted, though since all they do is turn and face you there's no real effects from this and no way to tell. All enemies apart from Wisps, and those spawned from traps will only spawn off screen.
Since SP and HP are restored upon levelling up, it is possible to use all your SP to get the final few kills to your next level, so you will then have an easier experience killing the monsters, and then have restored SP, which can save on Food etc.