I’ve not seen headsets being used a great deal with ‘hard’ IP phones but the times that I have seen them being used they’ve been the the same type that connect to traditional TDM PABX featuresets.
The curly RJ11 handset cable which connects from the bottom of the feature phone to the handset is removed from the bottom of the phone and plugged into a headset base. Another curly cable then goes from the headset base and into the bottom of the feature phone.
Obviously this wouldn’t work on ‘hard’ IP phones which do not use rj11 curly cables or other open connectors.
The headset unit I saw being used had the ability to switch between headset and handset by pressing or de-pressing a button.
With regards to the interfaces between the phones and the networks I have only ever seen ethernet RJ45 being used to plug into the LAN.