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)
You can use Markdown on Save, by Mark Jaquith.
Allows you to compose content in Markdown on a per-item basis. The markdown version is stored separately, so you can deactivate this plugin any time.