I think they knew he'd survive, and they didn't do what they did to kill him (it was more a lesson to show him he had forgotten to ask them to get out alive, and so he owed his life to their mercy). He's hanged for a very long time. If they wanted to kill him, they sure did an half-assed job of it. I think they wanted Mat to be their witness on the progress of the fight against Shai'tan, I'm pretty sure they considered his memories to come way to precious to kill him. The inscription on the ashandarei tells us they value memories as "the arrow of time" (I don't think that phrase referred to Mat's new memories, I think it talked of the price for their bargain).

I'm pretty sure they expected Mat. I think the Snakes told the Foxes they had sent him to them, and the Snakes knew Mat would survive...

I don't think Mat is in any way reliable to guess at their motives.

I think we're up for a few surprises when he gets to Ghenjei. I'm guessing they will be a part when he needs (or tries) to cheat them, but I think this isn't the whole of this episode. I seriously doubt Jordan had in mind to turn this into a pure action sequence style rescue. The secrets of the A & E (incl. their real motives.. we pretty much know they dislkike the Shadow and are unrelated to it. I doubt they'd do something to hinder Mat's destiny, personally.) and their tie to Mat is something that's been way too elaborately set up to be just a rescue, especially that the whole thing happens fairly late in the last book in the series (in RJ's plans, anyway).

It will be something as meaningful and momenteous as Rand's epiphany on DM, and Egwene's realisations about her role as Amyrlin in TGS, and her triumph that made her a wise woman among fools who had erred, fools who used to include her, but no more in TGS. I think what happens in Ghenjei will finish to shape Mat for TG, and it will be as momenteous and important. It's the pinnacle of his individual storyarc in the series, what's left after is his role in the LB that will complete his character development. Something similar will happen in Perrin's storyline as well in TOM (it's more obvious, he will be the Wolf King in truth, IMO - not only by having the wolves with him, but also by becoming mentally ready for it). At the end of TOM, both Perrin and Mat will be transformed, as much as Rand and Egwene at the end of TGS I think. And if Rand and Egwene are any clue, this will involve a big leap ahead in personal growth/wisdom.

Egwene had to give up a lot of her plans, and Rand had to give up a lot of his plans. By the end of TGS, they both understood that they were having it wrong. It may well be that Mat goes to Ghenjei intending to take revenge on the Finns and ready to cheat them and get the better on them, only to learn he musn't, that he needs them. He may go in facing enemies, only to get out with allies... A lot of what he blames them for is either his own fault (his own foolishness), the Will of the Wheel or Mordeth. If we look at Egwene/Rand, it sounds likely Mat will have to face that, and realise he's been wrong.