I'll describe my playthrough to this moment since I think that it may have caused a bug. In the investigation I performed the autopsy and put Kalkstein as the suspect, later accusing him. When I brought the results to the detective, he said that the culprits are Kalkstein and Ramsmeat and said to kill Ramsmeat. Since I already found Ramsmeat to be innocent (not sure how though, to be completely fair), I decided to postpone his killing and do other quests (side ones and collecting Sephirots). When I consequently found real Maarloeve's body, I told about it to Kalkstein and he offered to set a trap in the tower. However, I cannot find the tenth Sephirot. Kalkstein's notes say to find it at random, the book implies finding the Salamanders, and looking up on the Internet says to get it from Maarloeve. However, I cannot get it from him - I can only accept Ramsmeat's killing quest and talk about captain Vincent.

Also, when I talk to the captain, I can either tell him that Raymond is the Salamander leader or that Vincent is unrelated to Salamanders (also not sure how, the facts are just absence of evidence). And after choosing any of the options, the other one disappears, which I found weird.

Lastly, when I check my completed quests, I see that Kalkstein suspect quest is on his accusal stage (and not on setting trap for Azal as I thought it would be) and the investigation stage is on step where I wait for detective to sort out collected evidence, which was also supposed to be passed long ago.

So I ask - how do I work forward from this part and CAN I even work forward from it or did my shobby investigation job ruined everything?
Thanks.

Accepting the Ramsmeat job DID forward the events, thanks. Feel kind of stupid now for not trying to do it. My journal entry still shows Kalkstein as the suspect, but I don't think it matters now that the game clearly follows "Raymond is a fake" route.

Still, I wonder why can I tell Vincent only that he's not affiliated with Salamanders or that Raymond is the leader. One of those options gives the city guard ring, and the other one hints at him being a lycanthrope (assumption, pls no spoilers), so I was wondering how vital it is to skip one of these lines.

Don't worry - at my first playthrough I also didn't pick that quest for some time, being sure it would somehow triggered the fight between me and Ramsmeat. I finally took it when I was out of other options. :) At this point the ering is, iirc, useless. You could get it fairly quickly by finding proof of Vincent's innocence. This way you could get the ring which would be beneficial in some cases. "Raymond is the leader" marks the ending of the quest line, so it doesn't change the plot. In both cases you receive proof of innocence, just with different means.

I see. Thanks for the help.