The massive machine-type communications (mMTC) paradigm based on media modulation in conjunction with massive multi-input multi-output base stations (BSs) is emerging as a viable solution to support the massive connectivity for the future Internet-of-Things, in which the inherent massive access at the BSs poses significant challenges for device activity and data detection (DADD). This paper considers the DADD problem for both uncoded and coded media modulation based mMTC with a slotted access frame structure, where the device activity remains unchanged within one frame. Specifically, due to the slotted access frame structure and the adopted media modulated symbols, the access signals exhibit a doubly structured sparsity in both the time domain and the modulation domain. Inspired by this, a doubly structured approximate message passing (DS-AMP) algorithm is proposed for reliable DADD in the uncoded case. Also, we derive the state evolution of the DS-AMP algorithm to theoretically characterize its performance. As for the coded case, we develop a bit-interleaved coded media modulation scheme and propose an iterative DS-AMP (IDS-AMP) algorithm based on successive inference cancellation (SIC), where the signal components associated with the detected active devices are successively subtracted to improve the data decoding performance. In addition, the channel estimation problem for media modulation based mMTC is discussed and an efficient data-aided channel state information (CSI) update strategy is developed to reduce the training overhead in block fading channels. Finally, simulation results and computational complexity analysis verify the superiority of the proposed DS-AMP algorithm over state-of-the-art algorithms in the uncoded case. Also, our results confirm that the proposed SIC-based IDS-AMP algorithm can enhance the data decoding performance in the coded case and verify the validity of the proposed data-aided CSI update strategy.