To support increasing demands for real-time multimedia wireless data traffic, there have been considerable efforts toward guaranteeing stringent quality-of-service (QoS) when designing mobile wireless network architectures for ultra-reliable and low-latency communications (URLLC). One of the major design issues raised by URLLC is how to characterize QoS metrics for upper-bounding both delay and error-rate when implementing short-packet data communications, such as finite blocklength coding (FBC), over highly time-varying wireless fading channels. To efficiently accommodate statistical QoS provisioning for URLLC traffic, it is crucial to model and investigate wireless fading channels' stochastic-characteristics by defining and identifying new statistical QoS metrics and their analytical relationships, such as delay-bound-violating probability, effective capacity, decoding error probability, outage capacity, etc., in the non-asymptotic regime. However, how to rigorously and efficiently characterize the stochastic dynamics of mobile wireless networks in terms of statistically upper-bounding FBC-based both delay and error-rate QoS metrics has been neither well understood nor thoroughly studied before. To overcome these challenges, in this paper we develop analytical modeling frameworks and controlling mechanisms for statistical delay and error-rate bounded QoS provisioning in the non-asymptotic regime. First, we establish FBC-based system models by characterizing various information-theoretic specifications. Second, we characterize the outage-probability and outage capacity functions in the non-asymptotic regime. Third, we develop a set of new statistical delay and error-rate bounded QoS metrics and control mechanisms including delay-bound-violation probability, QoS-exponent functions, and the -effective capacity in the non-asymptotic regime. Finally, the obtained simulation results validate and evaluate our proposed controlling mechanisms for statistical QoS in supporting URLLC.