Direct growth of transition metal dichalcogenides over large areas within the back-end-of-line (BEOL) thermal budget limit of silicon integrated circuits is a significant challenge for 3D heterogeneous integration. In this work, we report on the growth of MoS2 films (~1-10 nm) on SiO2, amorphous-Al2O3, c-plane sapphire, and glass substrates achieved at low temperatures (350 C-550 C) by chemical vapor deposition in a manufacturing-compatible 300 mm atomic layer deposition reactor. We investigate the MoS2 films as a potential material solution for BEOL logic, memory and sensing applications. Hall-effect/4-point measurements indicate that the ~10 nm MoS2 films exhibit very low carrier concentrations (1014-1015 cm-3), high resistivity, and Hall mobility values of ~0.5-17 cm2 V-1 s-1, confirmed by transistor and resistor test device results. MoS2 grain boundaries and stoichiometric defects resulting from the low thermal budget growth, while detrimental to lateral transport, can be leveraged for the integration of memory and sensing functions. Vertical transport memristor structures (Au/MoS2/Au) incorporating ~3 nm thick MoS2 films grown at 550 C (~0.75 h) show memristive switching and a stable memory window of 105 with a retention time >104 s, between the high-low resistive states. The switching set and reset voltages in these memristors demonstrate a significant reduction compared to memristors fabricated from pristine, single-crystalline MoS2 at higher temperatures, thereby reducing the energy needed for operation. Furthermore, interdigitated electrode-based gas sensors fabricated on ~5 nm thick 550 C-grown (~1.25 h) MoS2 films show excellent selectivity and sub-ppm sensitivity to NO2 gas, with a notable self-recovery at room temperature. The demonstration of large-area MoS2 direct growth at and below the BEOL thermal budget limit, alongside memristive and gas sensing functionality, advances a key enabling technology objective in emerging materials and devices for 3D heterogeneous integration.