This paper addresses the tracking control problem for pure-feedback stochastic nonlinear systems subject to full state constraints, actuator faults, and backlash-like hysteresis. An adaptive finite-time control strategy is proposed, using radial basis function neural networks to approximate unknown system dynamics. By integrating barrier Lyapunov functions with a backstepping design, the method guarantees semi-global practical finite-time stability of all closed-loop signals. The strategy ensures that all states remain within prescribed limits while achieving accurate tracking of the reference signal in finite time. The effectiveness and superiority of the proposed approach are demonstrated through simulations, including a numerical example and a rigid robot manipulator system, with comparisons to existing methods highlighting its advantages.