MDA and Rothstein were the masterminds, and manipulated everyone else involved. MDA knew she could plan it with his help, Rothstein knew he could build the bomb. I think the $250K was for Rothstein's estate, and MDA would get a piece of it after realizing her dad wasn't going to leave her any $.
I bet MDA wanted Barnes in on it as a patsy or a third body, of sorts. So she went to him like, hey, kill my dad. Barnes talking about $250K is too much of a coincidence here, but they made such a point of making MDA and Rothstein so much smarter than everyone else that it wouldn't surprise me if she "incepted" Barnes in a way to make him think that $250k was run of the mill.
I believe Hoopsick when she says she got Wells involved. I believe Wells never believed the bomb was real until the timer started going off. I believe Wells only got involved out of a love for Hoopsick.
Eerie PA did a miserable job. When the guy is like: "Oh, that's weird, there's a van at the dropoff site. Let me do NOTHING about this". Are you serious?
I think when Rothstein realized that MDA killed Roden, he was like... oh shit, I gotta get ahead of this crazy person, and then started becoming the informant