I observed that my custom bash prompt does not work on
mc. How do I customize it?
The issue is that .bash_login files are only read when bash is run as the login shell. mc probably just calls a new shell which will read its startup from ~/.bashrc See bash documentation for details.
To make the shell run in a common way it is often suggested that you call .bashrc from .bash_login e.g.
if [ -f ~/.bashrc ]; then source ~/.bashrc fi
Read the INVOCATION section of the man page, it's there for a reason. MC is most likely not launching a login shell and you are only configuring your prompt for login shells.