A: You execute those things listed in the order shown, so Creeper elimination happens after drawing an extra card. James Baxter just makes everyone feel good. So if you draw a Creeper because of James Baxter, put it into play, and then draw to replace it. Then, after all that, the Creeper discard phase occurs.
So if a problem shows up while James Baxter is around, he gets rid of it for you, along with any other problems!* He’s just great.
* After getting rid of all Creepers in play, James Baxter then gets rid of all Hand and Keeper Limits in play.