Q: Can I remove the Powered By message at the bottom of each page, or the sponsor link at the bottom of the page of the demo page.

A: Yes you can remove these links.

You can use  joomla, the template included with the complete install and the component for free. And you are free to use and modify it as you like. I won't stop you from removing the links.

However I will only tell you how to remove these links in exchange of buying a license.