insert player into a page or post

Is it possible to insert a player into a page or post as well as the sidebar?

if I understand your question correctly, you want to be able to have some kind of shortcode in order to insert it in a specific page or post to display the player? if that is the question, then no, at the moment it is not possible to do so.

I am planning to do a major update and add more functionality to this plugin, such as being able to select audio files from library and etc, I will add your suggestion to feature requests and will implement it when I have free time.

I also found this plugin which allows you to insert widget into a page using shortcode. Hope that helps.