"Do the people of Azeroth know that the Burning Legion created the Lich King and the Scourge?"
I would say that it's probably not common knowledge, as in boring old villagers and farmers probably don't know it. Adventurous people like us, and the various militaries and their leadership? Yeah, we would probably know they have a connection. We likely don't know how deep that connection goes, but we would know that they were united at some point. Lordaeron saw them alongside demons, the Scourge and the Legion fought together at Mount Hyjal (even if the Scourge was only there to screw Archimonde over), and Sylvanas saw their relationship up close, in person.
The people of Azeroth wouldn't know all of the little details, but they would know that something was going on between the two.
"Where is Tyr?"
I've avoided this question for a few weeks now (as I'm sure you've noticed, rosencratz) but it's been asked enough that I think I should go ahead and be honest about it: We have no idea whatsoever. He apparently disappeared before the mess Loken started, because there was no trouble at his Temple at all. It wasn't touched, it wasn't bothered. It's simply empty and abandoned. He's... gone. And as far as we know, he plays no role in Ulduar. Key words there being 'as far as we know.' It could yet happen, but I have doubts.
It's possible they have bigger plans for him, like setting him up for opening Uldum or something of that sort. It's equally possible that he said, "Screw this, I'm outie" and proceeded to skip town. We really have no indication in either direction. All of the other Watchers have some story behind them, and you see how they tie into the other races and the rest of the world. Tyr? He just isn't there, or anywhere. Very odd.
"I realize that there are several places where "lore sources" contradict each other - in that case who do you follow?
Case: This morning I read the prologue to Christie Golden's Rise of the Horde. In it the eredar (specifically Velen, Archimonde and Kil'Jaeden) are portrayed as noble and spiritual - until Sargeras comes along to corrupt them.
A little later, while doing the Well Read achievement, I came across the book "Sargeras and the Betrayal" which pretty much reverses the situation and says that the eredar were "a demonic race bent on gaining power and dominance" - that they invaded and enslaved other worlds and turned their inhabitants into demons.
So which is it?"
Personally, I go with whatever was written most recently. The old RPG books are a good source of information... until those topics are touched on again by Blizzard. At that point, most of the little details will probably change, so I move on to the new source of information. In the case you described, the former is a more recent source of information than the latter.
The Eredar were originally an evil race that began the Burning Legion by turning Sargeras to the dark side, yes. That was changed. Sargeras turned evil first in the most recent iteration of the story and then went after the Eredar, and that's probably the one that will stick.
The old, original Warcraft lore is somewhat cobbled together, and while it's a solid story, there are bits and pieces that the creators of said story aren't very happy with and feel they could be done better. When it's time to fill in the details of things, usually when those things become relevant in World of Warcraft, the stuff usually changes a bit to better fit the world as it is now.
Go with what was written most recently. The in-game book Sargeras and the Betrayal was written prior to 2004. Christie Golden's Rise of the Horde was published at the tail end of 2006. Between the two, the information in Rise of the Horde is the most accurate depiction of Warcraft's current iteration.
Ask a Lore Nerd is here to answer all of your questions about the lore and story of the Warcraft universe. From the religions of the universe to the 'evils' of Azeroth, everything is fair game. If you want more in-depth answers to some of your questions, you may find what you're looking for in Know Your Lore.