Does it matter whether I use cloth, light or heavy armor? They all enchant the same things and the same amount. Wearing cloth doesn't seem to improve my magic dmg or ability. Whats the point of not wearing heavy armor?

Because you don't want to? If stamina is important for w/e build you have light is better. But heavy armor is easily what a mage should use for optimal build if you can enchant it with the same as cloth.

Well I think that Pure mages should wear cloth/light armor so you can move around and kite. If you want to tank then just wear Heavy armor and enchant it, don't forget to stack up on Magicka.

Alteration - mage armor perk. Also I don't believe there's any way to get a 100%regen/25%cost bonus on armor with enchanting. It's the in-game mage robes and uniques or nothing, if you want high regen.
I do believe a fully perked master-level armor spell is worth 300 armor, for 90 seconds. I don't know what the stats on fully perked dragon armor are, but at my current level I have about as much armor as a warrior would.

So, go for a regen-heavy build and stick with mage armor, OR go another route (stack 25% reduced mana cost items, maybe?) and perk into one of the armor trees.
Just keep in mind that no matter which route you take, you'll be made of glass. Since we have no real 'block' mechanic (ward is laughable against strong melee)

I have only 100 HP so I die in one hit regardless. I prefer non-cloth armor for looks. I plan to keep wearing arch mage robe and my 100% mgk regen mask as well I just want some cool shoes and gloves!