Balrog with the ring, would become pretty much like Sauron with the Ring, no plus.Why think that at all? We know that the Ring would work just fine for another Maia - Gandalf could have taken it if he'd wanted to, and Saruman of course wanted it for himself. The catch was that if they had done, they'd have ended up being just like Sauron, which was why Gandalf said he didn't dare have anything to do with it. As the Balrogs were Maiar and already extremely evil, it seems sensible to imagine that the Ring would have served one of them just fine as well. The only thing it wouldn't have done would have been to render them invisible when they wore it. And yes, a Balrog with the Ring would by implication have been pretty much unstoppable, because it'd have had its own considerable power plus most of that of Sauron.
The will of morgoth is vanished to the void, the only evil left is residual from his malice so no "impersonal" evil, its just residual influence. thats all-.As for the will of Morgoth - no, it didn't really work like that. Because Morgoth had been cast out of the world into the Void, he was outside time and so his will could no longer affect Middle-earth. However, an impersonal evil that had come from him was still around because before he'd been cast out, he'd expended most of his power to extend a subtle, evil influence over the whole world, so that it couldn't be removed by any means short of destroying everything.