-I don't know what Kruppe gets his random dreams from but I figure that's one thing K'rul does, since they seem to work in tandem sometimes. That being said, I sorta see the elder gods as manifestations of elemental forces and shit, and sorta natural to the world. Even without people worshiping him, he's a source of stuff.
If K'rul is any example, elder gods made people, realms, not the other way around (all the gods popular now seem to be humans or other races who ascended and stuff like that, and were sorta put in place as arbiters of stuff they don't necessarily have full control over).
-You'll learn about Rake's motives later. Well....in book 3, they set one motivation up that he gives. Later, another character comes to a separate realization...which, though more depressing, is probably the case (I don't mean that Rake is secretly evil or something XD).
-An azath is basically a manifestation of order or something. There are elder gods who don't fully get the azath, no one really knows for sure.
The basic function of an azath house you need to/should be able understand from GotM is to try to capture and hold powerful beings, especially ascendants. Because powerful beings bring about change and chaos. There's tons of other aspects of azath, but you'll learn them on your own....When characters are clueless about something in Erikson's books, you are supposed to be as well.
Also, you should know that Vorcan and Rallick Nom ended up in one. Not trapped by one, but actually inside of one. But you'll figure out why that matters later.
Finally, I would argue that the azath mirror a period of human evolution both in Erikson and in the real world (particularly, cities and kingdoms and such), but it takes spoilers from midnight tides to argue that.
-Crimson Guard are badass. The only guy who's ever killed one that I know of is Dassem Ultror, and he's 'dead.' Skinner, one of the others, came alive from a duel with Dassem, and Dassem has been mentioned in the same breath as Rake, the t'lan imass first sword, and other crazy strong warriors. Honestly don't remember everything, but I wouldn't be surprised if they had mages who could match some of the tiste andii.
Also, keep in mind that yes, tiste andii mages are good, but very few of them are anywhere close to Rake. Also, Rake might have Starvald Demelain to draw on as well, no clue on that (but he should since he's a dragon).
EDIT: As for Sorry....
Good question, actually, I'm not willing to give a single answer. But...
-Kalam's intimidated by her, and she hadn't given any signs of wanting to kill bridgeburners (besides officers, hehehe

). If there's a hornet's nest in your home, and you don't know how to get it out without getting stung, better learn to live with it.
-There's definitely a certain fascination. What's up with her? Is she pure evil?
-The bridgeburners, especially quick ben, kalam, and whiskeyjack, aren't run of the mill soldiers. Ben should be a high mage, kalam should be a leader in the claw, and whiskeyjack should be a fist at least. They (particularly whiskeyjack) accepted their place for various reasons, but that doesn't mean they don't know their own competence and importance. Better watch and see if Apsalar has any major motives or whatnot, you know?
-After the siege at pale, I think she was sorta bound to them simply in terms of her managing to survive, even if there wasn't much camaraderie.