1) Morokei is a Daedra artifact/Dragon mask and all Dragon masks fall under the "circlet" category. This means that they will in fact work Mage armor, and, it should be equip-able with the archmage robes for what its worth as well. Haven't tested myself though. Also, if it wasn't clear, you can use the heavy armor dragon mask as well I think. (source - http://www.uesp.net/wiki/Skyrim:Alteration)
2) Mage Armor works with any circlet and shield (mentioned in other comments - just confirming it works)
3) Nothing "destroys" the effect of mage armor from my understanding. If you have no cloths, cast mage armor, and then equip heavy armor, the full armor bonus + heavy armor will be applied. However, if you re-cast while its on, then the buff will go away.