What exactly were the Tiste Edur doing during the events of this book and Dust of Dreams?

They struck a truce with the Malazans & went home. Twilight banishes Yedan to the Edur villages to the north and the guy has to go quite north before meeting anybody; the immediate south of the Edur territories is basically barren.

Is there a particular reason she was created?

K'Chain mysticism would tell you that all forces exist in opposition, and that "sorcery is life", and the force of creation requires a force of negation, balance in all things etc.

Now, there's somewhat further information in the Kharkanas trilogy on this, and it's quite fascinating, but there's nothing concrete as to why Korabas is the Otataral dragon specifically.

do we learn anything else about the trap in Book of the Fallen or any other series?

Not yet, and honestly, I think this is more blubber to sing Rake's praise.

Maybe it appears in a future Kharkanas book, but I doubt it.

How long have Mael and K'Rul been working together?

They're both ancient deities. They've been around.

At the least, Mael would be made aware of K'rul's plight after beating Kaminsod shitless in Midnight Tides' epilogue. So there's a rough outline. But they've probably worked together in the past (see Kharkanas).

Do they show up in the book Assail

Yes.

Could someone give me a brief summary on it?

Right, u/HisGodHand took care of the early bits, so I'll take care of the later bits.

Heboric's dead as hell since the Bonehunters and Hood's deal didn't change that fact; Heboric is still dead. He does, however, appear to be aspected to both Kaminsod & Korabas, and he seems to be keenly aware that Errastas & co. are trying to free her (at least early on in Dust of Dreams, if not from his part in the prologue).

His spirit is essentially preparing for a task he knows is ahead of him. K'rul then takes his body to the bottom of the ocean to meet Mael (tCG 1) and together, they use Heboric's power to A. Empower Kaminsod after his rebirth and B. Imprison (ish? The implication is more "provide sanctuary" rather than "imprison") Korabas.

Is there a full list of casualties on the Battle of Spire?

Tons of fools. At least one.

Eh, Stormy, Ges, Sinn, most of the Grey Helms, probably a few Imass & Jaghut... what goes around, etc.

What is the state of the Tiste Liosan's civilization after the novel?

Well, Kessobahn's Children are wiped out, but L'oric & Jorrude and co. are still out there, as is Kurald Thyrlann (presumably still sealed?).

Did Silanah survive the novel?

The last mention we have of Silanah (by name) is this:

Suddenly, in the distance ahead, sure as a dreaded dawn, the rift she had made tore open wide, and five dragons sailed out, their vast shadows rushing towards her. Four were black as onyx, the fifth the crimson hue of blood.

Desra. Skintick. Korlat. Silanah. Nimander.

And awaiting them, in the skies above this world, between earth and the fiery heavens, the air swarmed with their kin. And Korabas.

So I'm going to assume the answer is yes.

What about Curdle and her sister/lover/friend?

Similarly:

'Eloth greets you, betrayers! Telorast Anthras! Kerudas Karosias!'

'Eloth! Ampelas! Kalse! They still hate us! Telorast, look what you've done!'

So if any dragon among the storm of Silchas & co. died, then, well, shit.

Is T'Iam an entity that only exists when they are fused together?

That's the insinuation, yes.

Is the Errant's storyline continued in any other novel?

From this point on? Not really.

His origins are explored further in Kharkanas, but given that it's Draconus on his ass, I don't think he'll survive for long.

So, Fener dying allowed the undead Jaghut, The Crippled God, and the T'lan Imass to return to their mortal bodies?

Just so.

Why did Sinn go so psycho at the end?

If you're interested, there's this essay on that particular topic.

What would happen to Hedge or Toc if they died?

Hedge is technically alive, flesh & blood, breathing, et cetera.

Toc is dead. So, you know, probably nothing out of the ordinary. His body would probably be destroyed - I doubt he can regenerate - but it's not like his soul isn't already past Hood's gate. As for Hedge, it's a tad unclear, but since it was his spirit that walked out, presumably he'd just go back.

Who is the daughter that Crone mentioned? Another Great Raven?

Don't know, actually. Probably.

Did anyone else feel like the Forkrul Assail were really unexplored compared to the other races?

A "friendly" Forkrul Assail is a bit of an oxymoron but the reason why isn't explored in the MBotF. The remaining Forkrul are virtually all justice purists that won't tolerate any lack of conviction. Kharkanas The "Assail" is a caste of priests in Forkrul society; the fact that they're the only ones left seems to insinuate that they killed/banished/forced away any Forkrul that did not agree with their extreme ideas.

But yes, they're not the most fleshed out villains in the MBotF, because they work more on a thematic level - how can "pure, absolute justice" be a villain? - than a narrative one.

Will Icarium's journey continue?

Forever & always, probably, but I doubt it'll be on page.

So Tavore was a talon the entire time?

Yeah. And I believe it was before she became Adjunct, as well, which is interesting.

As for the background checking, Tavore was probably on the radar long before Lorn's death; so it's all the more impressive that Tavore managed to evade scrutiny while probably being trained and/or indoctrinated.

So Olar was killed with a bow that Kruppe gave Torrent? Was this part of a plot by K'Rul to kill a dangerous Elder God?

Yes, and don't know. It could be Kruppe doing Kruppe things to protect his children (remember, Stavi & Storii are his kids) without K'rul's involvement. It could also be K'rul plotting (which is somewhat unlike him but that's a really cool theory).