Recently, benzotrithiophene graphdiyne (BTT-GDY), a novel two-dimensional (2D) carbon-based material, was grown via a bottom-up synthesis strategy. Using the BTT-GDY lattice and by replacing the S atoms with N, NH and O, we designed three novel GDY lattices, which we named BTHP-, BTP- and BTF-GDY, respectively. Next, we explored structural, electronic, mechanical, optical, photocatalytic and Li-ion storage properties, as well as carrier mobilities, of novel GDY monolayers. Phonon dispersion relations, mechanical and failure behavior were explored using the machine learning interatomic potentials (MLIPs). The obtained HSE06 results reveal that BTX-GDYs (X = P, F, T) are direct gap semiconductors with band gaps in the range of 2.49–2.65 eV, whereas the BTHP-GDY shows a narrow indirect band gap of 0.06 eV. With appropriate band offsets, good carrier mobilities and a strong capability for the absorption of visible and ultraviolet range of light, BTF- and BTT-GDYs were predicted to be promising candidates for overall photocatalytic water splitting. The BTHP-GDY nanosheet, noticeably, was found to yield an ultrahigh Li-ion storage capacity of over 2400 mAh/g. The obtained findings provide a comprehensive vision of the critical physical properties of the novel BTT-based GDY nanosheets and highlight their potential for applications in nanoelectronics and energy storage and conversion systems.