can Dallas use the MLE to just claim Brewer off waivers?
or does it not work that way?
No, but they could use the trade exception they have for Matt Carroll. If they can't negotiate a long-term deal, you can probably count on that happening. TP.
Didn't the Celtics get a trade exception from the Kings, or am I mistaken?
only 2.3M - not enough to cover Brewer's 3.7M
So he'd be taking a 1.4M cut to come here....well, we'll see if that's worth it to play on a NBA team submerged in history. 
Uh, no. The trade exception has nothing to do with what kind of contract we can sign him to, just whether we can claim him off waivers or not (we can't). So, if we sign him, the only thing we can offer is the vet minimum. He'll just be a free agent, and we have neither cap space nor the MLE or LLE.
Not sure how much he's leaving on the table in his buyout, but he'll probably come out even on the whole deal. I doubt he's giving up much more than a couple hundred thousand. Was reading today about someone else who was bought out, might have been Al Thorton, who agreed to forgo about $400k off his old contract. That strikes me as being typical for a buyout - more-or-less equivalent to what one of these guys would make on a vet-min deal for a few months.