Questions about Mark Waid's Flash run!

So I just picked up volume 1 of Mark Waid's Flash, and so far I'm half way through it and loving it. But I am a little confused on some things,

First, does this run happen after Wally becomes The Flash, or was there something between Barry's death in COIE?

Second, what's the exact order for pre Flashpoint flash between Waid, Morrison/Millar, and John's runs?