Wireless Internet access is facilitated by IEEE 802.11 WLANs that, in addition to realizing a specific form of CSMA/CA-distributed coordination function (DCF)- implement a range of performance enhancement features such as multi-rate adaptation that induce cross-layer protocol coupling. Recent works in empirical WLAN performance evaluation have shown that cross-layer interactions can be subtle, sometimes leading to unexpected outcomes. Two such instances are: significant throughput degradation (a bell-shaped throughput curve) resulting from automatic rate fallback (ARF) having difficulty distinguishing collision from channel noise, and scalable TCP performance over DCF that is able to curtail effective multiple access contention in the presence of many contending stations. The latter also mitigates the negative performance effect of ARF. In this paper, we present station-centric Markov chain models of WLAN cross-layer performance aimed at capturing complex interactions between ARF, DCF, and TCP. Our performance analyses may be viewed as multi-protocol extensions of Bianchi's IEEE 802.11 model that, despite significantly increased complexity, lead to tractable and accurate performance predictions due to modular coupling. Our results complement empirical and simulation-based findings, demonstrating the versatility and efficacy of station-centric Markov chain analysis for capturing cross-layer WLAN dynamics.