NEC option F relates to management contracting - a situation where project owner assumes most risks, hires a management contractor to manage work contractors. The management contractor is responsible for the work, and is paid a fee. This is very different to a traditional contracting system where the main contractor bears most risks and is responsible for the whole work.
If you understand the differences between governance structure in management contracting and traditional contracting, you will know exactly how party/representative/personnel selections are made. Some projects may have project managers representing the client, and some may have independent supervisors answering to project managers and/or the client. The botomline is that management contractors deal with the work, and they relate to the client either directly or through supervisors or both. You may then add consultants to these.
Appointment of client representative? This depends entirely on the client. The management contractor has no influence on this. Such appointments are based on the suitability of the representative to stated project objectives. You will find that experience, education, past performance, legitimacy, and relative compliance factors are the main determinants during selection. Further details and duties are available here: http://www.devon.gov.uk/kkbpv2-appendix18.pdf