I know that there exist nonnuclear EMP weapons, but these do not influence the entire world. Could someone build a device that creates an EMP that is powerful enough to make all mobile phones on the entire world stop working? How expensive would such a device be?
To take out all the mobile phones in the world, you would need multiple EMP explosions. The range of a single explosion is limited to the line of sight as the operative parts of the EMP are the gamma rays that strip electrons from the air molecules. (https://en.wikipedia.org/wiki/Nuclear_electromagnetic_pulse)
Secondly, the main way to take out mobile phones is to take out the base stations. These are far more vulnerable as they have antennas and a lot of wiring that can pick up the electrical pulse. They are also connected into the rest of the telco systems which are likely to stop working with an EMP. Without the base stations, you can't do anything with a mobile phone.