NGP, there's 2 ways to become ArchMage (head Wiz) of the Mages guild. From a WT.... First way (violent) :
"In order to achieve your last guild rank of Arch-Mage you must replace Trebonius Artorius in the Vivec hall as the guildmaster. This isn't much of a surprise if you're familiar with Trebonius, he seems a bit light headed to be head of the Guild. Once you've finished all of Skink's quests, and reached the rank of Master Wizard, talk with Skink to be given what amounts to Trebonius's pink slip (he's being fired by the Empire). Once you talk to Trebonius and give him the note, you will receive the last rank.
Similarily, if you've finished all of Edwinna's quests, talk to her about Trebonius and then talk to Trebonius about becoming the Arch-Mage. He will challenge you to a duel to the death in the Vivec Arena. He has some great equipment if you can manage to defeat him and become the new guildmaster and Arch-Mage." Second way (non-violent) :
"There is a non-violent way to becoming archmagister of the mages guild. If you do all of the mages guild quests, Skink in Tree in Sadrith Mora will ask you to deliver a letter to Trebonius from Ocato (spelled correctly this time). In it, Ocato asks Trebonius to promote you to arch-mage. Trebonius will, but he won't step down; you end up both being arch-mages, and you get a higher reputation bonus (+2 confirmed) than if you kill him. The downside is the only way you can get his equipment is by doing the dwemer and Telvanni quests he sets for you."
You don't have to do this now, you can at any point....I don't think you really have to ever. The only things you must do are the main quests.
As for Hasphet Antabolis...he's in the Balmora Fighter's Guild.