Two-dimensional semiconductors such as monolayer MoS2 combine a useful band gap with a thickness of three atomic planes, which places the entire carrier density within a few angstroms of the surface and makes them attractive both as transistor channels and as chemical sensors. We present a self-consistent ensemble Monte Carlo (EMC) framework for monolayer MoS2 built on the ViennaEMC solver, which couples a Boltzmann transport model to Poisson's equation with degenerate free-carrier statistics. The transport model carries wavevector-dependent acoustic, polar-optical, homopolar and intervalley phonon scattering within and between the K valleys and the spin-orbit-split Q valleys, together with remote substrate phonons, screened charged impurities and surface roughness. Every intrinsic input is computed from first principles for this work, the band structure of the K and Q valleys, the phonon energies, the sound velocities and the dielectric response, and the electron-phonon couplings from density-functional perturbation theory matrix elements at 34 explicit phonon wavevectors and from Wannier interpolation with the two-dimensional long-range treatment. The model therefore contains no fitted transport parameter and no coupling taken from another calculation, and its scattering rates are checked against an independent solution of the linearised Boltzmann equation with the same couplings. The EMC velocity-field characteristic feeds a one-dimensional channel model, verified against a direct self-consistent three-dimensional EMC simulation of the gated channel, which reproduces the measured transfer characteristics of a CVD monolayer device in air and vacuum. An ambient and adsorbate extension reproduces the measured conductivity response to oxygen partial pressure and the concentration dependence of NO2 and NH3 sensing of independent monolayer devices.