You can actually skip several of the tasks by moving on to later ones if you really want to cut your time spent on this quest line. Be aware that you will lose out on rewards by skipping tasks- particularly as, after you collect information regarding both Nepos the Nose and Thonar Silver-Blood, you will find something rather less pleasant than a curious local waiting for you in the Shrine of Talos- if you opt to do this, make sure you skip your reading forwards appropriately or you could wind up with a very, very nasty surprise.
When you enter the Shrine of Talos, you will see that, while not occupied for the most part, it is well-kept (relatively speaking). Eltrys is here, leaning on one of the pillars that supports the small roof over the Talos statue. As you approach, he apologizes- this is Markarth’s problem, and he didn’t really think it fair to involve others in it. Still, as both an outsider and someone who he credits with ‘looking dangerous’, you’ll apparently be able to accomplish what he thinks needs doing.
When you talk to him, requesting some sort of explanation, he tensely declares that he’s seeking some sort of explanation himself. The situation makes no sense to him- a woman is attacked by someone who obviously was working for the Forsworn, and the guard have done nothing but clean up the mess left behind. The blond man is upset and direly wants answers, but all he’s been able to find so far is more murder. He wants you to investigate and try to find out why Margret was attacked, who was behind the Forsworn attacker, anything, and he’s willing to pay you for whatever you can find.
At this point you can get a few explanations from Eltrys, though none of them are satisfactory.
Margret was/is not from Markarth, and it apparently showed a lot. If she is/was like other outsiders, she probably stayed (or is still staying, if alive) at the Silver-Blood Inn. He has no idea why she was here, what she was doing, or why the Forsworn would want her dead.
Weylin apparently was a worker from the mine area of Markarth, who spent his time smelting silver ingots and not much else. He stayed in the workers’ Warren down by the mine, but although Eltrys used to work in and around the mine himself the young man really doesn’t know anything about Weylin, who kept mostly to himself.