Channel State Information (CSI) provides a detailed description of the wireless channel and has been widely adopted for Wi-Fi sensing, particularly for high-precision indoor positioning. However, complete CSI is rarely available in real-world deployments due to hardware constraints and the high communication overhead required for feedback. Moreover, existing positioning models lack mechanisms to detect when users move outside their trained regions, leading to unreliable estimates in dynamic environments. In this paper, we present FPNet, a unified deep learning framework that jointly addresses channel feedback compression, accurate indoor positioning, and robust anomaly detection (AD). FPNet leverages the beamforming feedback matrix (BFM), a compressed CSI representation natively supported by IEEE 802.11ac/ax/be protocols, to minimize feedback overhead while preserving critical positioning features. To enhance reliability, we integrate ADBlock, a lightweight AD module trained on normal BFM samples, which identifies out-of-distribution scenarios when users exit predefined spatial regions. Experimental results using standard 2.4 GHz Wi-Fi hardware show that FPNet achieves positioning accuracy above 97% with only 100 feedback bits, boosts net throughput by up to 22.92%, and attains AD accuracy over 99% with a false alarm rate below 1.5%. These results demonstrate FPNet's ability to deliver efficient, accurate, and reliable indoor positioning on commodity Wi-Fi devices.