With the advancements in finite block-length information theory, short packet communication has received significant attention in the recent years. When devices are constrained to use short packets for communication in interference limited scenarios, it is important to explore the impact of interference on the performance of the system. In this work, we consider a two-user Rayleigh fading Z-interference channel (Z-IC), where one of the users causes interference. The work obtains closed form expression for the average error and throughput for prominent interference mitigation schemes such as successive interference cancellation and joint decoding using the framework of finite block-length information theory. The developed results take into account the packet length, rate and underlying channel model. However, the average throughput generally does not take random arrival of data at the users into account. To capture this, the stability region is characterized for the considered system model which requires the determination of probability of successful decoding at the receiver. The work also explores the impact of interference on average delay and average age of information (AAoI) for various interference mitigation techniques. The developed results help to explore the interplay between packet length, average delay and AAoI for the considered system model.