This paper reports a comprehensive study on the applicability of ultra-scaled ferroelectric FinFETs with 6 nm thick hafnium zirconium oxide layer for neuromorphic computing in the presence of process variation, flicker noise, and device aging. An intricate study has been conducted about the impact of such variations on the inference accuracy of pre-trained neural networks consisting of analog, quaternary (2-bit/cell) and binary synapse. A pre-trained neural network with 97.5% inference accuracy on the MNIST dataset has been adopted as the baseline. Process variation, flicker noise, and device aging characterization have been performed and a statistical model has been developed to capture all these effects during neural network simulation. Extrapolated retention above 10 years have been achieved for binary read-out procedure. We have demonstrated that the impact of (1) retention degradation due to the oxide thickness scaling, (2) process variation, and (3) flicker noise can be abated in ferroelectric FinFET based binary neural networks, which exhibits superior performance over quaternary and analog neural network, amidst all variations. The performance of a neural network is the result of coalesced performance of device, architecture and algorithm. This research corroborates the applicability of deeply scaled ferroelectric FinFETs for non-von Neumann computing with proper combination of architecture and algorithm.