This research presents a comprehensive and innovative approach to investigating the magnetisation and cross-field demagnetisation behaviour of high-temperature superconducting (HTS) coated conductors (CCs) in practical superconducting machines. This study introduces several novel contributions, including the operation of the machine in propulsion energy conversion mode, the exploration of harmonics interaction in a real electric machine environment involving CCs, and the extraction of these harmonics as cross-field components. A 2D electromagnetic-thermal coupled numerical model employing the finite element method (FEM) has been developed and validated against experimental data to simulate a partially superconducting machine. Upon magnetisation, the HTS stacks effectively operate as trapped field magnets (TFMs), generating rotor fields for motor operation. With a peak magnetic flux density of 462 mT of the trapped field stacks (TFSs) in the air gap, the average values of the fundamental and fifth harmonics of the tangential magnetic flux density experienced by the TFSs were observed to be 25 mT and 1.75 mT, respectively. The research has thoroughly examined the impact of cross-field demagnetisation parameters including amplitude and frequency on the demagnetisation of TFSs. Furthermore, the study has also investigated the magnetisation losses occurring in various layers of HTS tapes, encompassing the HTS layer, magnetic substrate layer, and silver stabiliser at different amplitudes and frequencies. Two tape structures, namely a semi-homogenised model and a multi-layered model, have been analysed in terms of magnetisation loss. Additionally, insights into the shielding effect and skin effect at high frequencies were obtained, offering valuable information on the performance of HTS TFSs exposed to high frequency scenarios, especially in high-speed machines for electric aircraft. The research outcomes are anticipated to provide valuable knowledge for the design and optimisation of HTS rotors employing TFSs in superconducting machines, contributing to the advancement of superconducting machine technology.