Mobility patterns are inherently linked to human nature (e.g., individual variability, temporal dynamics, behavioral factors, curiosity, social interaction), making mobility prediction a multifaceted and challenging problem that requires sophisticated models and comprehensive data. Machine learning (ML) models excel at predicting the location a person will be at the next time interval, but they often raise privacy concerns. To address these privacy issues while maintaining the benefits of ML models, Federated Learning (FL) offers a distributed framework that enables collaborative training of human mobility prediction models without requiring the sharing of highly sensitive location data. However, in the domain of FL for individual mobility prediction, prior work lacks a thorough understanding of the many factors that may impact the performance of FL-based prediction models. In this work, we provide a comprehensive study of the impact of various aspects related to human behavior, data characteristics, ML algorithmic solutions, and FL architectural structuring. We quantify the impact of such factors on effectiveness (accuracy) and efficiency (execution time, memory, and energy usage) of the prediction, revealing that, ignoring these factors lead to misleading result interpretation, and acknowledging them empowers both effectiveness and efficiency results.