1) What is the No-God? Was it known to the Inchoroi before Arkfall?
This one gets some sort of answer though there is no explanation whatsoever on why an Anasurimbor is required. BTW Nau Cayuti was not an Anasurimbor as far as bloodlines go. Hopefully this will be clarified in TBTSNBN?
I think Akka's dreams setting up Nau-Cayûti as Seswatha's son might have been a red herring, it's likely he was Celmomas' son all along.
4) Who was Anasurimbor Ganrelka?
The forefather of Kellhus is never mentioned in the Sagas or in the books outside the prologue. I was wondering why he was so inconspicuous compared to hi very famous brother (niece?) Nau Cayuti. Maybe it is just irrelevant...?
I've wondered about that recently as well, but it seems to have been left unclear if he was Celmomas' son by a previous wife or his younger brother (still plausible he'd be Celmomas' heir in the latter case if Celmomas had no surviving sons). Nau-Cayûti is mentioned as "the youngest of Celmomas' sons" at some point (can't remember where), but that doesn't ncessarily mean Ganrelka was the other/one of the others.
The argument of the 15-year age gap between Celmomas and Ganrelka is not a point against Ganrelka being his son, in my opinion: if you notice, Nau-Cayûti was 21 at his death and had been married to Iëva to 7 years at that point (per Akka's dreams), meaning he was married at the age of 14. If Celmomas married for the first time while that young as well (or even younger), he could conceivably have fathered Ganrelka soon after the marriage.
It seems that this one may remain unanswered unless Bakker decides to reveal it at some point (I think it's very unlikely it ends up being mentioned in the final series, though) or someone asks him about it.
6) What about the chanv? What is it? Where does it come from?
No answer. Probably Kellhus knew them, since he used the drug when "studying" Proyas in TGO.
I still haven't given up hope we might find this out in the next series. Maybe Akka does become addicted to chanv after his qirri runs out as Wilshire theorized in another thread.

Why Esmenet is "special"?
No answer that I could guess, and maybe there is no answer needed. But still I am a bit surprised that the almost only worldborn woman good for Kellhus was Achamian's wife (and Mimara's mother!!)
I'd also love to know the answer to that one. Maybe if we knew who Maithanet's mother was we could pinpoint what made Esmenet so special by looking at what they had in common.
I hope there was/is an actual believable in-world reason for this other than "narratively, Kellhus needed to take Achamian's wife from him to cause conflict" or Esmenet being intelligent (so were many or all of the other concubines mentioned in passing and not a single one of them managed to give birth to a surviving, non-deformed child).
Now that I'm thinking about this, I also remember that Cnaiür's mother had that child by Moënghus after he left that was apparently healthy (but was killed alongside with her anyway...). Presumably, she also had whatever made Maithanet's mother and Esment so special?
9)How did Mimara get the Judging Eye?
Why her among all the people? The one sent by Esmenet (or Kelmomas) to Achamian? Connected with question 8. Too many coincidences here, for me
I think we have to chalk that one up to coincidence for narrative reasons. It doesn't bother me as much as Esmenet being the only one capable of bearing Kellhus' children, especially because Achamian's explanation (of sorts, it's not like he knows that much about it) gives the impression that it is a thing that is not at all unprecedented (and while it may be rare, it makes sense for something that makes a person see with the eyes of the God).
I wish we had more information about it and am still hoping for it, though that probably will go nowhere by this point.
13) What did really happen on the Fields of Mengedda? Was the No God destroyed?
No answer. Kellhus hinted with Moenghus that the No God might have never been destroyed since It was speaking to him. Was the dream experienced by Achamian at the end of TTT truer than the "official" one? We do not now...many mysteries around Seswata yet...waiting for TBTSNBN??
I don't have any coherent theories here, sorry (someone who's more familiar with the series and has done several rereads will probably say something more helpful eventually). I think it might have disturbed the system holding Nau-Cayûti's soul in place and deactivated it somehow? Making it need another soul to be active again?
18) Where is the Heron Spear?
Not found yet. The new one was probably recoverd by the Mutilated, just as the Scald
Wasn't it taken by the Scylvendi at some point after the First Apocalypse? Presumably, the Mutilated would have been able to track it down and recover it after they took over.
21) Who killed Biaxi Sankas?
Is there any answer to this one? Was it Issiral? I could not find any solution.
I can't remember right now...I recall Theliopa asking Kelmomas if it had been him, but we don't have evidence for that in any of his POVs like we do for the other murders he committed/instigated. Maybe it was indeed Issiral...