Are we closer to an accurate 3D image of our galaxy using the Gaia billion star data set?

Gaia will give accurate parallax position with 1% accuracy for the nearest 100Million or so stars and 10% range estimates to the galactic center.

Good overview of the mission ESA gaia publication (pdf)

I'll provide a limited answer to a very broad set of questions.

Yes Gaia will tell us much about dark matter and its distribution. The improved census and more importantly, the distances and dynamics of stars inferred from their proper motions, will allow a much more detailed mapping of the gravitational potential of the local Milky Way.

In addition, Gaia parallaxes will be used to calibrate other Galactic distance indicators and stellar evolution models. Then one will have better estimates of distances right across the Galaxy to various kinematic probes, from Cepheids to RR Lyraes to globular clusters and planetary nebulae in the Milky Way and its satellites. From these, the "global" mass and gravitational potential of the Milky Way can be studied with more precision.

In terms of near the solar system - Gaia will not discover many new objects; its limiting magnitude is not very faint. However it will vastly improve knowledge of the orbits of many asteroids, including possible hazardous ones, and it will measure masses for many asteroids. e.g. Bancelin (2016, https://arxiv.org/abs/1608.08032).

Gaia will be very complete in terms of a census of nearby stars out to a limiting distance that depends on their spectral type. At the moment, the low mass end of the present day mass function is poorly known because of small sample numbers in the volume (only out to a few parsecs) out to which completeness can be assumed for very liw mass stars. For example, an M5 dwarf might have an absolute magnitude of 15. Gaia will be complete for such objects out to around 100 pc and in this volume there should be I guesstimate some 100,000 such objects. Gaia is unsuited though to discovering new cool brown dwarfs or free floating planets, because of its magnitude limit and lack of IR sensitivity.