This paper investigates the use of hybrid model-and-data-based deep learning on a recently proposed doubly-iterative turbo equalizer for handling inter-symbol interference (ISI) channel with single-carrier frequency domain equalization (SC-FDE). The receiver is obtained through a message-passing-based approximate Bayesian inference technique, known as expectation propagation (EP). Although this turbo-equalizer has been shown to behave asymptotically like maximum a posteriori (MAP) detection, finite-length numerical results suffer from drawbacks due to simplifying assumptions used during the modelling. Such limitations are partially mitigated by tuning heuristic hyper-parameters through robust learning algorithms. In this article, this strategy is further investigated with discussion on optimized parameters and with the use of an alternative loss function for training, or by adding further capabilities to adapt learned parameters to the channel state information.