SureAI

I started the quest by walking in the mine and getting a message like "There are many bad guys here, I must look for clues".
So I was following the marker, which led me to the place with two buckets, down a pit. I jumped in the pit, and there is absolutely nothing to do where the quest marker is. Furthermore, I am not sure how to get out of the mine (once you go down in the pit). There is a trapdoor where you find some undead miners and an Acolyte, but the acolyte is kind of strong and killed me. I can use a teleport stone, but I'd rather not, if possible.

Ohhh boy. That quest. I believe the proper way (or rather, the way you don't screw yourself) to start that quest is via the notice on the wanted board on gilad (not the wanted board itself, a readable notice on it) It'll warn you (when you start the quest this way) that you should not attempt this quest until you're level 11. As for the quest markers, don't follow those, explore! xD Ok tbh I don't know about your quest marker problem. If I'm not wrong this is the quest in steel rail mine? If it isn't ignore all the previous information. LOL xD

Well, with a lot of loads and saves and using most of my supplies, I got all the way to the diseased zombies. Those things really suck I am level 13, btw (made two levels in the mine).
Anyway, from reading this forum it seems that there are many ways to start this quest, so hopefully the whole thing isn't broken. If it is, oh well.

From what I know the mod-makers made it such that starting the quest the way you did wouldn't break/bug the game. To quote somebody on the forums "Nehrim isn't THAT buggy" so don't worry too much ^^ I went in there at level 14 came out at lvl 16, frost arrow level 2 saved my arse in there. You'll enjoy this quest, quite the interesting one this is.

Ok, I finished the quest.
I guess the only problem was that the marker was placed at the wrong position.
Overall, it was a very nice quest, except for the fact that you have to leave a lot of loot behind, especially when chasing that guy.. And without the frost and fire arrows, as well as the Paladin special blessing things, I probably would have had to just teleport away and come back a few levels later.

Which marker was misplaced?

When I got the quest by entering the mine and killing a few raiders, the first (and only) green marker was placed near (but not at) the entrance to the next level of the mine. Going to the next level, it showed the red marker at the exit towards the previous level (as if one of the quest objectives was in the water area as you fall in the pit, where the two buckets are).

Oh, that's a translation bug that will be fixed in 1.0.8.

How do you finish the quest. I started it in Gilead, and I am level 12 or so. I went through, killed the Master Miner or whoever the guy was at the end, and then exited, but it is still in my quest log. Did I miss reading something? I have slaughtered everything in the dungeon (silver bow sneak attack one hit kills lol!). Hope I didn't kill the wrong person (everyone attacked me, well, most of them that I didn't kill in one hit).

Yes you missed reading something...

[+]

In the forge area with the master armorer boss guy there is a book or a note (note I think) that details what you need to do next. Once you read it you will receive a pop-up message telling you what you need to do to complete the quest.