I am playing a Khajiit Archer with focus on smithing / light armor / bow / sneaking / lockpicking / pickpocketing

So, i was wondering. Does your skill level actually do anything apart from giving you access to certain perks? As far as i can see the stats of the items produced by smithing are fixed and not skill dependent. What about weapon damage? Does it increase with increased skill level or does it just depend on your perks? Is lockpicking getting easier with skill? questions... questions....

Not sure about lock picking, but weapon damage and armor rating go up with skill level. My Elven sword started at 16 and is now 18 and I didn't upgrade it yet.

I know that in all the spell skills, the higher your skill, the less it costs to cast spells in that type of magic. Also, weapons like OH/2H/Archery, as well as Armors get more powerful as you level them higher. I'm not sure about all the other skills.

Your Enchanting skill determines the percentages and figures involved with your new enchantments, so for example when my Enchanting skill was low I could only get about 10% Frost Resistance on an armour piece, even using a Grand Soul Gem. Now my Enchanting skill is higher, I can get 15% and higher.

The Smithing skill seems to affect how much you can upgrade your armour - for example I picked the Steel Smithing perk early on, and when my skill was about 30ish I could improve Steel armour to "Superior." Now my Smithing skill is 69 or so, though, I can improve Steel armour to "Flawless."

I'd imagine Alchemy is also affected in the same way. You can probably get higher damage/heals and longer duration on your poisons and potions. I've not really done Alchemy yet though so I can't say for sure.

Skills and perks both affect damage etc. in general, though.

yes

tested with 2h weapons. Very minimal difference between very high and very low skill levels. Its there but the real power is in the perks. Pity, really, since I would rather have them affect effectiveness and have perks give special abilities. No biggie since I always expected the vanilla system to be modded anyway.