Approximately how wide is each time zone?

The time zones as originally defined are exactly 15 degrees of longitude wide. Distance between the limiting longitudes is at a maximum at the equator, and diminishes to zero at the poles.

The equator is about 24,902 statute miles long, so at the equator the time zones are about 1037.6 statute miles wide.

The Prime Meridian, or Greenwich Meridian, is the line of zero degrees longitude, and this same line on the other side of earth, 180 degrees longitude, is the International Date Line as originally defined. The Prime Meridian and the IDL are at the centers of their respective time zones, and the remaining time zones fit in accordingly.

There is no international law regulating the placement of the time zones. Nations all over the world have made changes according to their individual needs. This makes perfect sense, especially for nations that straddle the IDL. It makes no sense for a single state to have to deal perpetually with one part of the state being a day ahead of another part.