This paper explores the evolution of Radio Access Network (RAN) architectures and their integration into Non-Terrestrial Networks (NTN) to address escalating mobile traffic demands. Focusing on Low Earth Orbit (LEO) satellites as key components of NTN, we examine the feasibility of RAN function splits (FSs) in terms of fronthaul (FH) latency, elevation angle, and bandwidth (BW) across LEO satellites and ground stations (GS), alongside evaluating performance of Conditional Handover (CHO) procedures under diverse scenarios. By assessing performance metrics such as handover duration, disconnection time, and control traffic volume, we provide insights on several aspects such as stringent constraints for Low Layer Splits (LLSs), leading to longer delays during mobility procedures and increased control traffic across the feeder link in comparison with the case when gNodeB is onboard satellite. Despite challenges, LLSs demonstrate minimal onboard satellite computational requirements, promising reduced power consumption and payload weight. These findings underscore the architectural possibilities and challenges within the telecommunications industry, paving the way for future advancements in NTN RAN design and operation.