You don't cast spells while running. You have to stop, cast the spell, then continue running.
The way you get spells off when you're aggro kiting is to cast your snare spell on the mob first, and keep that active. Get a feel for how long it lasts and at what point you need to recast it. For example(this is just my experience and since we're different levels you'll have to adjust the spells you cast accordingly), when I'm aggro kiting, I'll cast dooming darkness(snare), then run forward a bit, stop(this is how you can cast spells without getting hit. The snare will slow the mob down, and if you run out of spell casting range, then start clicking the spell gem it will cast as soon as the mob is in casting range, which should be plenty of room to get the spell off), cast venomous breath. Once venemous breath is cast I send my pet in. After that I run forward a bit more and cast splurt. That's a fast casting spell and usually gives me time to throw a low level poison DoT on before I have to run again. Once venomous breath wears off, I recast that, then recast dooming darkness. Now, dooming darkness hasn't worn off by this time, but I know that once venomous breath wears off, dooming darkness is about 75% done, and recasting before the DoT wears off resets the spell, so by recasting dooming darkness before it wears off, I can keep the mob constantly snared. And as far as gaining aggro, I've found that poison based spells are just about the most effective type to hold aggro.
To turn off taunt on your pet you need to bring up the pet window if it isn't up already(you should always keep this window up when using a pet by the way as it gives you several useful commands and a lot of information at your fingertips). On the main menu bar, in the middle should be a button with a stick person icon, that will bring up the pet information window. Once you have that up, there is a button that says Taunt. Clicking that button will toggle your pet's taunt off and on. You should get a message from your pet when you click this button saying either "Taunting attackers as usual master", or "No longer taunting attackers master". You can also type /pet taunt off to turn off taunt.
Shadow compact does not heal you. It takes HP from you and transfers them to your target. You have to cast a lifetap on the mob to regain the hitpoints you lose from casting shadow compact on your pet.
The key to surviving while you're aggro kiting is to keep the mob snared at all times. Having spirit of the wolf cast on you helps, but don't count on it as there won't always be a friendly caster around to help you. If you can, try to get an item with either spell haste or extended range focus effect. Those will help greatly. They may be out of your price range for now, but I'd suggest saving up for them.