Is there any accepted standards regarding how sheet music or piano scores are stored mathematically instead of as images or PDFs?
Everything thereof are digitally represented such as in an XML or something, so when one needs, he or she can easily manipulate the music itself instead of just editing a PostScript image.
Any such format existing and the license to use to carry music scores?
You are looking for musicXML. It's the common format used by the major music notation software packages, like Finale and Sibelius.