3) What is the function of a music video?

Definition of a music video:  A film or video of a recorded song, often showing the musicians performing or showing images that illustrate the lyrics or following the mood of the song.


The first and main function for a music video is to promote the artist and it's song. 
With artists from big label records, the purpose for promoting the artist in the video is to make the label more money, however not all genres music videos have the same purpose.

An example of music genres that are not made to visually promote the artist would be music such as: Electronic, House or Dubstep, This is because the music is made for dance and usually the listeners interested in those genres will focus on the music rather than what is going on in the music video, because of this, most dubstep videos don't even have music videos, and if they do, it is rare to see the actual artist in the shot.

Some music videos are made for the simple purpose of symbolism. Artists will either use the music video to their advantage to declare something about themselves, prove something or announce something.

Another function of a music video would be to evoke emotions and moods onto the audience. Some artists will create illusions or use a lot of CGI in their music videos to get people thinking about themselves or the world around them. For example, the CGI can make the artist appear in a broken world.

Music videos are most definitely used for representation, sometimes in a bad way...
Some artists use the opportunity of music videos to present themselves as sex objects

A music video i personally think is considered a good example of the video forms is Mark Ronson - Uptown Funk ft Bruno Mars.

This is because, the mood the song gives combined with the music video, makes the whole song very lively and energetic, making the audience feel quite happy and want to dance. The choreography in the video is quite simple yet very effective and motivates the audience to also dance along.
The video is set in roughly the 1980's as we are presented with the clothing of the artists and dancers, also the setting of the pawn shop and the props such as the car they are seen dance around.
Uptown Funk