Never mind. I had saved the game right after killing the guy in Gnaar mok and right after posting this I went back and tried again and this time the plan worked like a charm. I ran to Caldera, got in the mages guild building before a guard caught me, fast traveled to balmora, got into the club before a guard caught me, killed all the bad people, ran to pelagiad, and she cleared my bounty. i tried about 4 times before posting this and kept failing, then went back and tried once more and made it. Go figure..
How the hell do you complete some of these quests where you're supposed to kill someone and to do so you must commit a crime?

I know one can taunt a person into attacking you, but not when your speechcraft skill is at 15. I mean I can't recall how I did it last time, but this time I figured with the Boots of Speed I'd just out run the guards until I got back to Ahnassi (or whatever her name is that wanted me to kill the guy in Gnaar Mok. IIRC, if you get back to her, she clears your name but you can't outrun the guards. THey're as fast as me despite not having boots of speed (which seems just wrong to me).

Then there is the quest where I am supposed to kill "bad people" in Balmora for the guy at fort Moonmoth trying to clean up corruption. Again, no luck getting them to attack me, so it's kill them and commit a crime or no competing the quest.

I could've sworn I completed it last time but maybe not I dunno. This is irritating as hell. Guards that can run as fast as you can magically enhanced. Bullshit.

And another irriating thing LOL. I'm typing on this laptop and every time my hand or finger just touches the touchpad my cursor jumps somewhere else so that my typing moves all over the place. Is there any way to PERMANENTLY get rid of that damn thing? i never use it, I always use a mouse, and usually use a real keyboard, but not when I'm mobile.

Anyway, I had a good plan. Kill the dude in Gnaar mok (actually ending up killing four because there were four in the room and they all became hostile once i attacked the guy i was supposed to kill), then I would run to Balmora, kill all those bad people in the club, and then run to Pelagiad and report to whatever that kajiit's name is and she would clear my crimes. Nope. Once a guard starts running after you, you can't lose him. DAMMIT>

If you have an insane amount of Luck (in other words, if you used the Super Potion trick to get your Luck into the quadruple digits), then yes, you can taunt a person into attacking you even if your speechcraft is that low.

Alternatively, if you don't want to break the game that much, you can just use a spell to fortify your Personality and Luck, which should boost your effective Speechcraft. Alternatively, if you have access to Fortify Skill effects (obtainable in Mournhold or in the Bloodmoon area), you can just fortify your Speechcraft so that it is no longer 15. Have you tried using a Calm spell on the guard? Alternatively, you could try using a teleport spell (like Divine/Almsivi Intervention) to try teleporting away.

(Would Invisibility work in this situation? Chameleon?)

You're thrown into a heterogenous medieval-type fantasy society with its own rules and laws, and you're trying to survive there, assuming a role you make up yourself. Whatever you do, you must face the consequences. To attack someone (except in self-defense) is against those rules, and the authorities are trying to hunt you down.
If you play a law-abiding role, you don't accept quests requiring you to attack someone else. If you're playing a criminal, you better think about how to get away with assassinations, thefts, etc. first. To do so you can try to run away or use stealth or bribery - or klll the guards (if you are strong enough).
Excellent role-playing experience - don't you agree? :-)

On a more practical note: You might argue that there's no point in offering quests if you can't complete them, or that you miss too much of the game contents if you accept only a small number of the quests which are contained in the game.
I'm playing different characters with different personalities, ethics and objectives, and every single one of them gives me a different game experience in the same world. There are the classical ones, fighter, mage, thief, but why not play an assassin, a revolutionary or an anarchist, a guy aiming for a career with one or several of the races, factions, guilds, etc - or a pacifist (one of my most interesting roles).
My daughter used to play a "herb-witch" (collecting all possible herbs and creating all kinds of potions) or a water-character who likes to swim, dive, collect pearls, and to explore underwater locations. And my son once played a character whose aim was to kill all guards, and in fact the whole population of Morrowind (I don't think he ever succeeded, because he lost interest after a while :-)).
The bottomline is that you're probably better off exploring what you can do (and dtgreene is doing this, too, in a very different way, by stressing the game functionality to its limits and beyond) than complaining about what you can't do.
It's up to you.

THey're as fast as me despite not having boots of speed (which seems just wrong to me).

That does seem wrong. What's the use of being the blind Flash if the guards are all the same?

I see your point.
I myself have committed my crimes always and only when nobody was watching, and if necessary, I have paid my fines or got rid of them with the help of the Thieves Guild. In order to get away from an attacking guard, you can always use an Intervention (or Recall) spell - not a permanent solution, I know :-).
I just looked up the UESPWiki concerning crimes ([url=http://www.uesp.net/wiki/Morrowind:Crime]http://www.uesp.net/wiki/Morrowind:Crime[/url]). According to that entry (sections Crime + Punishment) it looks like you can manage your crimes and bounties quite well (keep your bounty below 5000). But I'm not sure that's applicable to your issue.