I haven't tested with plugins. But I doubt if it would work. It works great for Vanilla Jekyll with Markdown.

Does it output a static website?

This is independent of your jekyll site generator. What it does is, gives you an editor for your files inside _posts. It understands yaml matter and saves in Jekyll format.

Is it possible to write the posts using mark down instead of the web editor?

The web editor isn't rich text. You edit in Markdown in the web editor. It is an easier way of creating new posts.

Not so much a question but a suggestion, you should have a version of this hosted on AWS/Heroku so people can see it live.

Totally agree. I had thoughts on hosting a demo site. I'll do it.