Adjectives used to describe all sorts of things are also used to describe music, but I'll give you a few that are often associated with music.
1- Happy music. (right? what other adjectives are applicable here?) – upbeat, cheerful.
2- Sad music. (Any other adjectives?) – minor key, bluesy, melancholy.
3- Some music without any song. (Is instrumental good enough?) – In most cases, yes.
4- Mild music. (How can I describe it with one adjective?). – If you mean to be derogatory: bland, muzak. If neutral: light. Perhaps MOR (middle of the road).
5- How can I describe the kind of music I hear in a party? What adjectives? – Depends on the type of party, maybe: wild, rockin', danceable, lively.
6- How can I describe the kind of music I listen to when I am studying? The kind of music which is not annoying when one studies and even helps. – ambient, low-key, background.
7- How can I describe the rhythme of a piece of music? – Depends on the type of music, maybe: jazzy, steady, syncopated, leaden, jaunty, hot etc.