For sneaking, do you get any benefit from "muffle" spell and "muffled movement" perk, if you are not wearing any armor?

Are robes armor? Not in the classic sense I know, but i don't know how the game "sees" it.

I'm not sure what the hard values are, maybe if your not running?

Clothes don't count as armor,as far as I am aware anyhow.
Muffle reduces the amount of noise your armor makes while sneaking.So if you are not wearing any armor you don't need muffle.