I found out about the lack of magnitude errors trying to use a S/N cut for astrometric solutions, so I think that adding the errors is certainly worthwhile. Simply propagating errors from the flux errors (dmag = 2.5/ln(10) dflux/flux) is fine; for any source with significant flux the errors are going to be close to symmetrical. I think that we should use that formula and write the Gaia ref_cat in "standard form" (while awaiting the decision on Jim Bosch's proposal); as this is a once-off conversion for any given input catalogue I don't see that having some special-case code is much of a problem. Adding another column would move the onus onto pipeline code, and I would not be in favour.
It would be good to include the BP and RP photometry at the same time (with errors) as e.g. it'll allow us to make refraction corrections to the astrometry even if we can't use the values for photometric calibrations.
I don't think that it's likely that Gaia will add symmetrised errors; at that point (S/N <~ 3) the pdf is not fully characterised by a simple variance (as the distribution is not Gaussian) and the gain is small. As they point out, in that case you should be working in flux units, but we simply don't care.
I think that the conversion from their flux units (e-/s) to calibrated fluxes and magnitudes (including AB, and thus Jy) is described in https://gea.esac.esa.int/archive/documentation/GDR2/Data_processing/chap_cu5pho/sec_cu5pho_calibr/ssec_cu5pho_calibr_extern.html (e.g. just above equation 5.36).