Just made the "Larrius Varro tells a little story" quest by taunting one (and getting two more into the fight) and just plain killing atleast 3.
Then after that I immediately teleported to Fort Moonmoth and a guard tried to arrest me. Since I didnt want to sit in jail for all eternity nor did I want to pay the fine I resisted arrest in the futile hope of Larrius Varro fixing that little problem.
He said he had fixed it, gave me the ring and let me go. Then I went through the front door (reluctant of using a Almsivi Intervention scroll) and got attacked by the guards again!
That bastard Larrius Varro has betrayed me by tossing the guards at me! Guess he wanted to make it harder to track the murders back to him...

Anyways, how do I fix this? I got a PC however I can not use any console commands... Am I screwed?

Hopefully you've got a recent save. Take this quest in small bites.
If you're a member of the Thieves Guild.First challenge Thanelen Velas, the Smith upstairs. If you got tagged for a crime, pay it off and you should be clear. Then go back and go downstairs past the bar and challenge the Scout (whose name I usually forget.) Kill her and get back to th TG and if you got tagged and pay your bounty.
Then go call someone out in the barroom at the council club. At worst you will only have to kill four baddies which doesn't amount to the 5000gp that gives a death warrant that means the guards will try to kill you forever.
The best way IMO to do this is by putting a Mark spell at the South Wall Club, kill the bad people one at a time whenever possible, Recall to the South Wall, then pay the bounties.
When you finish the dirty deeds use Divine Intervention to get to get to Fort Moonmoth, duck inside fast, use Invisibllityand run inside to Larry Varro (one of the sleazier bastards of the game IMHO) who should lift any bounties you've incurred. After you kill off the bad guys in the Council Club barroom go straight to Larry Varro not to the TG.
Make sure that your bounty is NEVER more than 5000 drakes. Keep it toa minimum.
I don't know if this helps. There are console fixes but since I've never had the problem I've never used them. Someone will be along and tell you what to do.

You should do it exactly as Anais says, only taunt them instead of attacking them. After a 4-5 successful taunts, they should attack you and you won't get a bounty. That's how I usually do it and Varro gives you an extra book for completing the quest without getting caught.

This is true. Always taunt to provoke the enemy into attacking. I should have mentioned that. (High Speechcraft or a lot of bribes help here.) If not an outright attack will provoke everyone in the Council Club into the fight, including the bartender for a bounty of >6000 gp (death warrant.) But get rid of the Smith first, then the scout.
When you pick your fight in the barroom everyone in the bar will attack, except the bartender may not.

Well... Unfortuantely I do not have any saves before that...

Is there some "Ring of Console" mod for Morrowind? If there is, could I perhaps just "kill" (cheat-kill) the guards and then resurrect them/let them respawn?
That would hopefully solve the problem...

Can you somehow talk to Varro about your bounty, or does it not even say you have any?

Why can't you use the console? If it's the old vista problem there are fixes, like deinstalling your IR drivers.

The dialogue with Varro should definitely have set your PCCrimeLevel to 0. Maybe fighting with the guards has increased their Fight level? I'd suggest you just use the Almsivi Intervention scroll to escape them, and staying away from the fort for 3 in-game days should eventually reset them (I think...)

Next time get Mark and Recall and set a Mark right in front of Larrius Varro. Then after you finish up in the Council Club, just Recall back to him. This will avoid any encounters with the guards. There may be a separate script for fighting/killing guards that Varro can't fix when he removes the bounty for killing the "bad people". That's just speculation on my part mind you.

Personaly I'd use a frenzy spell on one of the guys in the bar room. One guy attacks and they all attack. If you are of a respectable enough level they shouldn't be a problem. The key here is to wait for them to make the first strike. Even if they initiate battle, it will still count as assault if you make the first hit when there are witnesses around, even if the witnesses are also hostile. By the time you kill the first one the rest of them will have taken plenty of swings at you so this won't be a problem. If you did it right you should be able to marily strole out of the council club without fear of the gaurds. They issue with Larrius Varro not removing your bounty sounds like just one of many little bugs in the game. As awsome as Morrowind is it's FULL of them.

Yes, either frenzy or taunt. And you can use the furniture to your advantage, so they can't all get to you at once.