I recently got the Nightingale armor and fell in love with the "+25% One-Handed Damage" enchantment on it. Is that a standard fortify One-Handed enchantment? Can it be disenchanted and learned? Also, assuming it can be learned, if you have the Double-Enchantment perk can you double down on the same enchantment or do the two effects have to be different?

You can learn that enchantment, but not from Nightingale armor. It can't be disenchanted. There are other random items out there that will have it. That's the standard one you mentioned.

You cannot double up on the same enchantment, unfortunately.

Excellent, thank you for the answers. So a standard Enchant One-Handed will give you the increased % of damage, then? Also, can you enchant beyond +100% damage?*

*cumulatively over multiple items, not on a single item, clearly.

Yeah, the enchant one-handed is a % of damage, not a skill raise. You can also get above 100%, though I'm not sure of exactly how much. Using standard maxed enchanting (no alchemy), you can get 40% each on a necklace, ring, gloves, and boots (I think).

you do get those buffs on other armour sp id save the ightinggale coz its the best looking stealth armour