There's a useful history of the BT Carphone service at :
http://cellnet.illtyd.co.uk/carphone-1959
Most of your questions should be answered there.
I maintained the base station end of the "System 3" in the North of Scotland from about 1977 on. Five VHF FM channels with Pye T100FM transmitters (forced-air cooled QQV06-40 in the PA, and Storno receivers as I remember). It closed down about 1980 and was replaced by System 4 based on German TeKaDe kit.