I found TextMate support for GitHub flavored Markdown
http://github.github.com/github-flavored-markdown/
and now try to install (lots of ruby stuff needs to be installed, struggling..)
then will try to have live preview feature.
Perhaps, it is possible with a shortcut key, but is it possible on every modification without saving the file?
Yes, it's possible to make a preview without file saving, just run Bundles > Markdown Redcarpet > Preview
or here is a shortcut for this: ⌃+⌥+⌘+P.
To use a keyboard shortcut properly, I recommend to uninstall original Markdown
bundle.