Orthogonal Time Frequency Space ({OTFS}) modulation offers significant advantages over Orthogonal Frequency Division Multiplexing ({OFDM}), particularly in high speed environments. Hence, we consider {OTFS} transmission over high-Doppler Non-Terrestrial Networks ({NTN}). However, OTFS-based systems inherit some deficiencies from {OFDM}, such as its high peak to average power ratio, the bandwidth efficiency loss due to the cyclic prefix, and the sensitivity to the carrier frequency offset. Against this background, we harness both Multi-Band Discrete Fourier Transform-based Spreading (MB-DFT-S) and Index Modulation ({IM}) in our {OTFS} system, termed as MB-DFT-S-OTFS-IM. More explicitly, 1) DFT-S has been shown to reduce the {PAPR}; 2) {IM} is capable of improving the throughput by harnessing it in the Delay and Doppler ({DD}) domain; and 3) MB-DFT-S-OTFS-IM provides frequency diversity gain, which benefits the tolerance to carrier frequency offset. Furthermore, we propose a {PAPR} reduction method based on a Deep Learning ({DL}) Autoencoder ({AE}) architecture for both hard- and soft-decision detection, where the encoder is specifically trained for minimizing {PAPR} and the decoder is conceived for accurately reconstructing the transmitted signal. Finally, we extend the proposed {AE}-aided {OTFS-IM} scheme constructed for a practical {NTN} channel model, representing a variety of satellite-to-ground schemes.