I use a headset on my phone, and can hear lots of humming or buzzing

Phones are DC powered, un-earthed, and susceptible to mains AC noise. This can normally be solved by providing a better earth to the phone by using a SHIELDED twisted pair cable, and ensuring that the socket the cable is connected to has a path to earth.

(Note: if the phone has 2 network ports, and one is connected to a PC, using an STP cable between the phone and PC will be the easiest solution)