Spells only create sound when they're actually cast (unless you have the illusion perk which negates the sound). Spells create light whenever they're selected, and even more when they're actually cast. (This is very similar to the self-illumination via pipboy in Fallout 3).
Given that you can't score sneak attacks with spells in the first place, keep your mage hands in your thief pockets when going in for a sneak stab.
I was wondering if by attacking bare handed, you increase your 1-hand (or 2-hands) weapon skill mastery.
I played through the start of the game unarmed (Khajit), and never increased my one-handed or two-handed skills.
[...]do the Khajiits's +15 claw bonus mean that every one-hand weapon below damage 15 is useless?
If only comparing pure damage, yes.
Does, as example "Backstab" skill bonus apply just to any 1-hand weapons, or to barehand too?
The sneak perk Backstab applies to one-handed weapons, which bare-handed is not.
Can I, say, do a stealthy istant kill from behind when unarmed? Like breaking the neck maybe?
You can sneak attack while unarmed (and with a two-handed weapon) for extra damage. If you do enough damage to kill the opponent in one shot, you may be treated to a special animation. IIRC, there's an unarmed neck snap one.
Best Answer
I think the power attack is just as silent as a normal swing, the grunt/yell is purely for effect. I went up behind an enemy and whiffed a bunch of power attacks on purpose and he had no reaction whatsoever, then I finished him off with a power attack and a nearby patrolling enemy didn't react.
I have to add an addendum to this:
Power attacks can sometimes push your character forward a little bit on the swing, and this can cause you to be detected before the attack connects, making you lose the sneak attack bonus. Make sure you are standing far back enough for this to not happen.