Will wearing skill fortifying items to boost the skill above 100 stop that skill from levelling up

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.

**your loot is random generated in most cases with some special items being set or fixed loot tied to a location or quest/person. i have tried the same save first then enter,then reenter to see if the loot changed and this didn't change the trigger but entering a different dungeon then reentering did reset the loot trigger. Random but would suggest you stop wearing your enchanted helmet of " give me crap i can't use " : P as a consolation here is a link to a invisable chest ingame that you can loot every 2 days,crap loads of stuff including specials like what your looking for and does NOT trigger stolen...

hope this consolation prize eases your bad luck,but i wish you luck in future quests : )