To add to this question, the Destruction robes you can buy also have a regen increase, if I disenchant these the enchantment has both Fortify Destruction and Regen.
Now if I want to enchant something with these does it add both of these enchantments? and If so, does it count as 2 enchantments or with the extra enchantment perk, can I add a 3rd?
There are two types of enchantment per magic school
1) "bigger" reduction in spell cost
2) "smaller" reduction in spell cost + mana regen
1 and 2 are each a single enchantment (even though 2 has more than one effect).
I tend to skip (2) and go for as many (1) enchantments as possible. With high enough enchanting you can get to 100% reduction. At that point you wouldn't even need magicka regeneration. With the level 100 Enchantment perk, there's enough enchantment slots to make 2 schools of magic absolutely cost free.