Can I replace the WYSIWYG editor with a markdown editor? If so, what plugin can I use?
I'm not sure about the version of Markdown, but here's some plugins
I use markdown-for-wordpress-and-bbpress to get wordpress to render posts and comments in markdown format.
For editors, I prefer markdown-quicktags. It has a bunch of auto-complete features, and seems to be the most actively updated markdown editor plugin. You might also try wmd-admin for the wmd editor (Same markdown editor as the stackexchange) or wp-markitup (not markdown specific)
Not mentioned is WP-Markdown or Markdown on Save Improved.
I did look at Markdown for WordPress and BBPress but apparently it hasn't been updated since 2008 and never went beyond version 1.0.