Can't answer the first question either, but for the second one:
I think it's a combination of two things. First, he might indeed have been too scared. The last thing he knew from the outside world was how the Valar got rid of Morgoth and all his servants they could catch, including, presumably, all other Balrogs. How could be have known that the situation was less hostile outside afterwards? He could have learned it from the Orcs after they invaded Moria, but there is no indication that there was ever an actual contact between them.
The other reason could be that, after the end of Morgoth, he had no master anymore, and no purpose. Sauron must've known about the Balrog after the invasion of Moria, yet the Balrog did not join him (or was never asked to), so Sauron apparently was not sufficient in rank to be a master. Alone, the Balrog indeed seemed to not have any own initiative beyond keeping his doorstep clean from non-evil.
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