This thesis focuses on a cutting-edge area of research, which is aligned with CERN's mainstream research, the "AWAKE" project, dedicated to proving the capability of accelerating particles to the energy frontier by the high energy proton beam. The author participated in this project and has advanced the plasma wakefield theory and modelling significantly, especially concerning future plasma acceleration based collider design. The thesis addresses electron beam acceleration to high energy whilst preserving its high quality driven by a single short proton bunch in hollow plasma. It also demonstrates stable deceleration of multiple proton bunches in a nonlinear regime with strong resonant wakefield excitation in hollow plasma, and generation of high energy and high quality electron or positron bunches. Further work includes the assessment of transverse instabilities induced by misaligned beams in hollow plasma and enhancement of the wakefield amplitude driven by a self-modulated long proton bunch with a tapered plasma. This work has major potential to impact the next generation of linear colliders and also in the long-term may help develop compact accelerators for use in industrial and medical facilities.