This work presents the combined geometry-adapted passive Time Reversal (pTR) and Decision Feedback Equalizer (DFE) technique for time-variant shallow-water communications. We consider high data rate communications between moving source and/or receiver array, implying geometry changes (i.e. source-receiver range and depth changes). By using waveguide invariant properties of underwater channels, such geometry changes can be partially compensated by employing a proper frequency shift on the probe impulse response in the pTR processing. We then refer to the geometry-adapted pTR as Frequency Shift pTR (FSpTR). With dense and long receiver array, a pTR-based technique possessing pulse compression property can eliminate Inter-Symbol Interference (ISI) problem in multipath static channels. However, with a practical-size array and time-varying channels, a residual ISI always exists. Hence, in this work, we apply an adaptive DFE to further mitigate the residual ISI from the FSpTR, and call the technique as FSpTR-DFE. Performance of the FSpTR-DFE is evaluated using both real experimental and simulated data, where an information rate of 2000 bps and BPSK signaling are considered. The experimental data was collected during the RADAR'07 sea trial, where a slow moving source, free drifting receiver array, and carrier frequency of 12.5 kHz are considered. For the simulated data, the south Elba site and carrier frequency of 25.6 kHz are studied. A moving source with speed of 1.5 m/s and a fixed array are considered. The results show that a considerable performance gain is obtained when the FSpTR-DFE technique is employed as compared to the FSpTR.