Massive ultra-reliable and low latency communications (mURLLC) has emerged as new and dominating 6G-standard services to support statistical quality-of-services (QoS) provisioning for delay-sensitive data transmissions. To measure the freshness of updated information, age of information (AoI) has recently formed as the new dimension of QoS metric. Since status updates usually consist of a small number of information bits but warrant ultra-low latency, integrating AoI with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">finite blocklength coding</i> (FBC) creates an alternative promising solution for mURLLC. On the other hand, to solve the massive connectivity issues imposed by mURLLC, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unmanned aerial vehicle</i> (UAV) has been developed to significantly enhance the line-of-sight (LOS) coverage while guaranteeing various QoS requirements. However, how to efficiently integrate the above new techniques for statistical delay and error-rate bounded QoS provisioning in UAV systems has been neither well understood nor thoroughly studied. To overcome these challenges, we propose FBC based statistical delay and error-rate bounded QoS provisioning schemes which leverage AoI as a key QoS provisioning technique for mURLLC over UAV mobile networks. First, we develop FBC based UAV system models. Second, we build up AoI-metric based modeling frameworks to upper-bound peak AoI violation probability using FBC. Third, we formulate and solve FBC based peak AoI violation probability minimization problem. Forth, we jointly optimize peak AoI violation probability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -effective capacity and characterize their tradeoffs. Finally, our simulations validate and evaluate our developed schemes.