I disenchanted the novice hood and novice destruction robes. When I get the perk later on, could I enchant something with both if those? Would they stack or are they considered the same enchantment

I think those are different enchantments.

What I should have said was can I use another singular magicka regen or destruction cost reduction enchantment with the combination enchantment from the robes.

The "Fortify Destruction and Magicka Regen" found on destruction robes is a single enchantment containing both effects, it could be added to a chest item, (and only a chest item), along with another enchantment.

*Except Dunmer shoes take chest enchantments instead of foot

However the fortify school enchantment is weaker then the individual fortify destruction and magicka regeneration is fixed at 10% on custom items. Fortify magicka also can not be placed on chest items. You could however put "Fortify Destruction & Magicka regeneration" singular enchantment with Fortify Destruction on a chest item.

Yes, you can, although I've found that the combo enchantments that you obtain from disenchanting college robes don't tend to be very strong. You might unenchant a master mage robe that has 150% magicka regen plus a 22% reduction fro destruction (or whichever school), but when you go to enchant an item with that combo effect the stats become much smaller, more like a 12% reduction on destruction and a 70% reduction on magicka cost (can't remember the exact numbers though, so I might be off). I guess they do that so you can't make an enchantment of your own that will be stronger than certain in-game items.

But yeah, technically you could enchant an item that has both the regular "fortify magicka regen" enchantment plus the "fortify magicka regen + fortify destruction" enchantment, and it would combine them together to make an item with an especially strong fortify magicka regen enchantment. However, I've generally found that this is not particularly worthwhile, at least for me. For one thing, I can't remember for sure, but I don't think the items that they can be enchanted for (i.e: head, body, hands, feet, etc) overlap perfectly, althoug I might be remembering wrong. Also, I think for the items that they do overlap on it didn't end up being that much more powerful in the end. I think there were certain in-game items that still beat the combo, which I found just a little disappointing, but oh well.

That said, if you experiment with this, I'd be very interested to hear what your results were.

Thanks everyone!