First of all, what is the difference between daggers and swords? Double weilding them both works the same, except swords do more damage. Is there something I'm missing here? Why would people even use daggers?
Second, is alchemy necessary for stealth? On my Mage I stole all of the ingrediants from te Arch-Mage and randomly picked some and made soooo many potions bur my Alchemy level didn't go up at all. I don't understand what Im doing wrong.
Third, any tips for this type of character? I've never played one before.

Daggers are for stealth. No and I'm not sure why.

They function the same, daggers might be faster. In addition, there's a sneak perk that does 15 times normal damage with daggers.

Daggers do significantly more stealth damage once certain perks are taken, and I'm pretty sure they have higher base stealth damage than swords anyway. Daggers also (obviously) swing much faster than any other melee weapon available, so they can be good for quickly putting down foes that have already been weakened by archery/magic.

From what I've noticed, alchemy starts off slowly but skyrockets as soon as you learn most of the ingredients' effects. If you're playing a stealth character, then poisons and health potions are the order of the day.

As for tips, most of them are rather obvious. Stick to the shadows as much as possible, and extinguish any light sources you can (ie. grabbing torches from walls). Poisons can also be quite useful, and their versatility can seriously help in combat situations. Fighting a mage? Hit them with a poison that stops mana regeneration or drains it entirely. Fighting a huge warrior? Hit them with some frostbite venom or with a potent poison to level the playing field.

Opinions on armour vary from player to player. The heaviest you want to get playing stealth is wearing all light armour. Heavy armour is obviously worthless if you're trying to sneak past anything more powerful than a skeever. Clothes can also work, or a mix of light armour/clothing if you are so inclined.

Thanks alot!

I believe daggers are also silent where as larger weapons make more noise.
http://www.uesp.net/wiki/Skyrim:Sneak
"Heavy armor and large weapons make more noise; daggers are silent, meaning that enemies are not alerted to your dagger swings, even missed ones."

In the Sneak perk tree, you can get a 15x multiplier with backstabs while using a dagger. Add in the Shrouded Armor Gloves and it jumps to a 30x multiplier. This allows to stealthy type to simply one-shot that one enemy which you simply cannot sneak passed without drawing too much attention to yourself.

While focusing on stealth/assassination...

1 v 1: Dagger.
1 v Many: Sword & Board.