When requested, simulated Gaia parallax and proper motions are computed. The errors on these are estimated using the PyGaia toolkit. The errors are computed based on the apparent and extincted Gaia G magnitude, and the V-I colour. The errors are scaled to different mission lengths using the same simple power-law scaling as PyGaia. For a mission length of 22 months (the length of data collection for DR2) the errors appear to be reasonably close to the measured errors.
If you are interested in just one model of the inner Galaxy your default choice should probably be the chemodynamical model of Portail et al. (2017). This model is the only model that has different kinematics for different metalicities.
If you are interested in different dynamical models of the inner Galaxy you should use the dynamical model of Portail et al. (2017). With this you can change the bar pattern speed, alter the stellar-to-dark matter ratio in the inner galaxy using the mass-to-clump ratio, and change the central mass. Most of these choices can give pretty poor models of the Milky Way though, so be carefull! The best of the these dynamical models was used as the basis for the chemodynamical model.
The fiducial galaxia models are more appropriate outside the central 5kpc of the Galaxy. They are are also useful as comparision to an axisymmetric model in the central region.
You should not use the Portail et al. (2015) models unless you have a good reason. These have been superceeded by the 2017 models.
More detailed information on the models can be found here
The photometric constraints are applied before extinction is applied. This is for efficiency purposes to avoid having to compute extinction for every star that may enter the survey. If you only have a faint magnitude limit it is straight forward to apply this again offline after the catalogue is created. For the bright limit or the colour constraints, if you are working in a high extinction region, then you should liberally increase these when generating the catalogue, and then apply them offline.