Can the pole position winner in F1 choose which side of the track he wants to start from?

No. A certain circuit will always have the pole position on the same side of the track, although the side varies from circuit to circuit, often depending on the direction of the first corner. No, they must start from position one on the track. Sometimes this can be the diry side of the clean side.

The dirty side is the part of the track which is not the "racing line" and usually has less grip, which will be worse for starts.

The clean side is the part which is on the racing line and has more rubber on the track and so has more grip, i.e. better for starts.