Fully microscopic many-body models based on the Dirac-Bloch equations and quantum-Boltzmann type scattering equations are used to study the carrier dynamics in monolayer transition metal dichalcogenides (TMDCs) under conditions as typical for applications as lasers, diodes or saturable absorbers. The carrier-carrier scattering is shown to be happening on an ultra-fast few-femtosecond timescale for excitations high above the bandgap. Once the carriers have relaxed into quasi-equilibrium distributions near the bandgap, the scattering is slowed dramatically by phase-space filling and screening of the Coulomb interaction. Here, the scatterings and resulting dephasing of the optical polarizations happen on a 100fs timescale and lead to similar broadenings as found in conventional III-V semiconductor materials. Also like the case in III-V materials, the carrier phonon scattering times are found to be in the picosecond range. The scatterings are shown to allow for gain spectra as needed for good lasing operation. It is shown that the weak interaction between the two bands associated with the two different sub-lattices can potentially allow for simultaneous lasing at two different frequencies. Strong absorption and ultrafast carrier relaxation could allow for TMDCs to be used in saturable absorption applications.