Who sent the severed arm with the money?

It may be "cool' but it is not plausible. Look, the Chechens had a good thing going with Marv, the bar, and the drop. But then money starts to disappear, and the chief suspect is Marv. Because it would be a hassle (to say the least) to find and train another Marv, the Chechens decide to send him a warning in the form of the severed arm and the stolen cash, a kind of "Don't *beep* with us" comment. They are willing to monitor Marv's larceny until they can come up with an alternate arrangement. (Notice that the Chechens do not ask why the money is wet when Bob returns it.) Marv fails the test, of course, with the Super Bowl drop, but by then the Chechens have found a suitable replacement and Marv is dispensable.

I think it was the Chechens. Throughout the whole film, although it only becomes clear when we learn about Marv's past, he is acting out an endgame, knowing that robbing the bar will go one of two ways - he will get the money and be able to disappear off to a new life or he will get caught if it goes wrong. After he phones Eric and realises the SuperBowl robbery hasn't come off, he sees someone approaching behind his car and shuts his eyes waiting to be killed as he knows it is all over. He actually says to one of the brothers earlier "we are dead already, we just don't know it", suggesting he knows that he probably won't get out alive, but he just feels the need to push on with the robberies as he wants out of his present life one way or another.