According to the wording on page 36 you can cast direct damage or magic missiles through Skink Priests and Troglodons. Then it goes on to say a Slann "can cast magic missiles, even if his own unit is engaged in close combat (provided that the Arcane Vessel is not)" Does this mean that we can or can't cast direct damage through an Arcane Vessel when the Slann's unit is engaged?
Yes, you can. There aren't any restrictions on casting Direct Damage spells from within combat. Magic Missle is the only spell type with an explicit exception to casting from within combat. (BRB pg. 31)
You can always cast direct damage spells if you're in combat, but you can't cast them AT an enemy unit in close combat. Magic missiles have the specific exception in the BRB that the mage can't cast them if his unit is in combat. EDIT: Rychek wins the race!