Do they scale with one handed or increase one handed at all? Or would fighting with them completely halt combat progress?

I don't think that they add to the one-handed skill but the strength of them is definitely based off your one-handed skill.
With my Khajiit character (weird for me because i used to be a beast-race hater) i love using my bare hands to slaughter low level enemies, i did the entire Bleak Falls Barrow quest with my bare hands haha

They don't. It's an unarmed bonus only.

I have no clue if unarmed combat increases any stat, but I do know it can be really nasty if your a Khajiit with high armor rating gauntlets and have the associated perk.

+15 unarmed bonus, does not scale to anything. If you want it to scale, take the heavy armor prk that allows you to do damage with your gauntlets. Then it'll scale with your heavy armor skill.

There is a gloves enchant that has +unarmed damage. You can get it off of some (unique?) gloves that drop in a specific place. This enchant, the perk and the Khajiit bonus, you can actually get pretty good damage.