[Nate]

1)Where'd Elum go after Abe's Oddysee?
In-universe? Anywhere. There's not just one Elum, after all. They're a species.
Out-universe? OWI couldn't fit Elum in to AE for memory programmatical reasons. He wouldn't have suited MO as he/they served Abe and MO was (theoretically, at least) Munch's game.

2)Why is his food preference honey?
Because it's sweet and yummy? Because there seems to be bugger all else to eat in Paramonia or Scrabania? Do we need a reason?

3)If Elum is(as it says in Oddworld Abe's Oddysee) Abe's pet... just, how? I mean, if Abe was raised in Rupturefarms, how'd he meet Elum?
Pretty much what AlexFili said. Also, regard the term 'pet' loosely; he serves Abe and helps him out, but he's not a pet in the way of a cat or a dog that someone raises from birth for companionship.

4)Why is he afraid of bees, but not Sligs, Slogs, anything else?
He's not afraid of bees; he quite happily sits under a hive and eats dripping honey. What he doesn't like is being stung; that makes him groan and try to shake them off.