1. - No, luck does nothing for quests
2.
3.
4.
a. - Yes, it combines with others so you have dual slayers. I don't believe it gives 4x against undead with an undead slayer weap.
b. - See 4a
c. - See 4a
d. - No, the only Fey Slaying item is the pixie staff thingy... there are individual slayers though, but haven't seen Pixie on any.
e. - Slayer is slayer