The asterisks at the end of filenames mean the same thing as the asterisks when you do $ ls -a: "executable file". NERD_Tree doesn't know or care about GIT so, in other words, neither the asterisk nor NERD_Tree are directly related to your problem.
But NERD_Tree may be indirectly related to your problem: by default it doesn't change the working directory when you enter different directories. So it's possible that you do :! git commit in a different directory than the one you think you are in. One that is not under version control.
Type :pwd to know where Vim is, if it's not the right directory you can change it with :cd /path/to/your/versioned/directory.
If you are often in the wrong directory you can add two lines to your ~/.vimrc to force Vim's working directory to always be the one containing the current file:
set autochdir
let NERDTreeChDirMode=2
The first is a Vim setting (:help autochdir), the second is a NERD_Tree setting (:help nerd_tree).