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Plaque of Domination:
The plaque can be used at the beginning of any enemy turn. Each enemy Wizard within 18" that can draw a line of sight to the plaque or the unit it is with must take a Stupidity test.

So if there is a unit of infantry, with two wizards inside, does that unit take 2 stupidity tests, one for each wizard?

And if a wizard fails the unit he is with also stumbles forward and can't do anything, right?

Would the wizard take the test on the units highest LD, or the wizard's.

The Becalming Cogitation:
At the beginning of the enemy's magic phase, before any spells have been cast, nominate one enemy Wizard within 24" of the Mage Priest. Any power dice that roll 6 made by the Wizard are discarded, and do not count towards irresistible force result.

So do they still count towards miscasting? (I assume not, I'm just asking to be sure.)

What about things like Grand Hireophant Khatep's Liche Staff?

The Liche Staff:
Khatep can declare that he is using the Liche Staff immediately after rolling the dice to cast a spell, even if the result indicates irresistible force. If Khatep uses the Liche Staff, he re-rolls all the casting dice used in the attempt. Khatep can use the Liche Staff once per turn.

Is that to say that all 6's are removed on the first roll and he simply re-rolls the ones that weren't sixes again and if there are any more sixes those are also removed? Because remember:

Any power dice that roll 6 made by the Wizard are discarded

It could go either way on that though, I'm not sure.

EDIT: Now that reading that effect again, it seems like it wouldn't. Because he re-rolls all dice used in the attempt, even if they were discarded.

As far as Cogitation goes....

If the die is discarded, it does not count. It will not count for IF, it will not count for Miscast (which only results when you roll 2 or more 6's).

As far as the Staff goes...

Its a reroll, so the original 6 never counted, and is therefore not discarded. The FAQ also stated when 2 magic items seem to be in contrast the player whose turn it is decides which order the magic items take effect.

The above is 100% correct

Anyone know the questions I asked about Plaque?

Yes, you take two tests for the two wizards, and if you fail one the unit stumbles forward

The plaque causes every Wizard in Los to take a test that you can draw a line to.
Basically if you can draw a line to it without hitting anything then it takes a stupidity test.
Lets say there are 2 Wizards Sleeves in a unit of 30 spearmen but one is in the 2nd rank.
You couldnt draw a line to that one as you would hit the model in front of him.
However and this is where the description gets firmly placed in the Basket Case.
A slann is a large target so therefore could technically see over the models for Los on the Wizard in the 2nd rank.
Personally. i would make the front rank one take one and the 2nd rank one take one on a 4+.

Thats why you use a slaan for thta banner from his throne he can draw TLOS to anyone.