Yes Muse supports Typekit fonts. This should help: http://museinsider.com/how-to-add-typekit-fonts-to-your-muse-site.html.
In the example given in the link, only the tags "header' and "body" have been used. Is it important to stick to only these tags or we can name them as something else also ?
For example, I would want to use more than 2 fonts on my website, and I would need to add different tags to be able to use those fonts.
I do not know the answer to your question regarding Typekit.
For Typekit help you should post questions in the Typekit forum here http://help.typekit.com/.
For Muse help you should post questions in the Muse forum here http://forums.adobe.com/community/muse.
There is Lynda.com training here http://www.lynda.com/Typekit-tutorials/Up-Running-Typekit/85873-2.html. You can get a 7 day free trail to Lynda from http://lynda.com/trial.
Some other links that look helpful:
Europe, Middle East and Africa