I've got a few questions.

1. Being someone that primarily uses Destruction but also Alteration and Conjuration, is it better to get Master Robes of Destruction or Archmage's robes?

2. Let's say I got a Mage's Circuit (+70 magicka)
Can I enchant this item so that it will reduce the magicka cost of Destruction? In other words, can I enchant items that already have an enchantment on them? (Considering I have the perk that allows you to have 2 enchantments)

3. What type of shoes do I wear..?
I don't seem to be able to find any shoes that aren't classified as armor. I don't want to wear armor because I am taking the perk that boosts the armor rating of the Alteration skills.

4.Has any of you found good enchanted mage (non armor) apparel and staves out there in the world of Skyrim? I would prefer not to enchant my own items.

5. (Edit) Another question has sprung into my mind. How does the perk for Alteration bonuses work? Is it only activated if you have absolutely 0 armor on you (No items that give you any defence)
OR
Is it only the piece of armor where you wear on your chest, like a shirt or something.

Addressing point 3, have you tried going to Solitude and going into the clothing store? I haven't been myself, but I imagine it would work similar to the clothing store in the Imperial City. I can't suggest anything for the rest, I don't play mages...

I will check to see if any boots suit me. Thanks.

You should have been given boots when you became a member of the college.

Not to impinge upon your way you want to play, but enchanting is an important and esential branch to the 6 schools of magic. (Some debate on whether alchemy is a science or school of magic)

I honestly have not gotten 1 single pair of enchanted cloth boots or gloves in the last 60 levels on master difficulty. The basic enchantments are so poor even on master level gear that you will always suffer mana problems.

While the armor bonus from alteration is nice, unless you are playing a melee mage it is mostly pointless. Taking 2 shots to die vs. 2.5 (at master diff) is a relative pointless argument. Don't expect amazing results with alteration.