How do they affect the stability of the bow and DMG output
You get the ATK and Stability values listed on the Arrows added to your ATK. You also get the stats as well which is the case with all sub weapons excluding ones which are actually main weapons(Knuckles and Magic Devices). You also get whatever element the arrows are, so Fire Arrow makes your attacks fire element.
Other than that I don't know of any other bonuses to them. They are almost always the best option for sub equipment for Bows and Bowguns, especially when you can take advantage of an element with them.
ManaKhe- Lvl 285-300 Enchanter(gotta get dat Mblade and Stoneskin) ManaSel- Lvl 240ish Monk ManaLock- Lvl 147 Servant