Do mages need armor or will alteration an restoration spells along with enchantments suffice?

Well, from the screenshots I would say, no. All mage models have been wearing robes.

I'd say it will definitely suffice. It is up to you if your mage wears armor or not, but they certainly don't need to wear it.

Edit: They probably get some kind of bonus for not wearing armor.

I heard that armor restricts magicka regeneration.

Some people play battlemages with bretons that wear heavy armor.
Some people play mages that don't wear light/heavy armor, and rely on magic shields from the alteration school.

I'm pretty sure you can play a mage with or without armor.

dont be coward.. be a mage.. burn everything that comes near you... armor / shield spells are for the weak

You can do whatever you want

Based on what I've read on the forums (take with grain of salt, or as expert advice) is that a pure mage is harder in the beginning, but will be powerful in the later stages.
A warrior will be easier in the beginning, but not as powerful as the mage in later stages.

Not sure about rogues.