if the glue was applied to a stone on the tip of an arrow, and the arrow was fired at someone with the intention of sticking to them...would that be possible?
I understand attack penalties would apply, and that if the stone was ripped off before it had a full round to set it would be useless
RAW, no. Ammo is destroyed when used. And either the stone wouldn't stick to the arrow or the glue would harden before it hit.
what if 1 person applied the glue and another person fired the arrow?
Attaching a stone to an arrowhead seems like a good way to screw up your shot royally. In any case, the glue needs to be applied and pressed for a round to set. If you shot the arrow and managed to hit the target with the stone, it'd do what any other stone would do--deal some bludgeoning damage and bounce off.
This is assuming that the GM doesn't conclude that the glue would harden after a round of exposure to air anyway; in that event, you'd have very little time to shoot the arrow once the glue was applied. It would be a reasonable conclusion.
Besides, throwing the vial as a called shot to the face seems like it'd be far more effective as a combat trick.