Hello, just looking to sort this out.
I'm looking to make a melee mage of sorts, and was curious as to figuring out if the One-Handed weapon perks effect Bound weapons, and if bound weapons tat are single handed will level the one handed abilities. My gut says yes, but then again my gut was wrong on my last test most of the time so I can't really trust it.
I can guarantee to you 100% that they do.
I checked my damage on my bound sword before and after I placed a perk in one-handed. The damage
did go up. I also get critical hits with my bound swords from my perk point in the Sword branch. My Decapitation and dual-wielding perks also work on bound weapons.
After taking the Conjuration perk called "Mystic Binding", I noticed that my bound swords now do better damage than my un-improved ebony swords (aka not improved through smithing).
YES, your one-handed perks will work on bound swords. As a side note, My "Overdraw" perk also applies to my bound bow.
My one-handed skill has gone up from 59 to 61 while exclusively using bound swords. Bound swords do improve your one-handed skill.