  We apply AnalyticLC, an analytic model described in an accompanying paper, to
interpret Kepler data of systems that contain two or three transiting planets.
We perform tests to verify that the obtained solutions agree with full N-body
integrations, and that the number of model parameters is statistically
justified. We probe non-coplanar interactions via impact parameter variations
(TbVs), enabled by our analytic model. The subset of systems with a valid
solution includes 54 systems composed of 140 planets, more than half of which
without previously reported mass constraints. Overall we provide: (1) Estimates
on physical and orbital properties for all systems analyzed. (2) 102 planets
with mass detections significant to better than 3 standard deviations, 43 of
which are lighter than five Earth masses. (3) 35 TbVs significant to better
than 3 standard deviations. We focus on select systems showing strong TbVs,
which can result from either interaction among the known transiting planets, or
with a non-transiting object, and provide: (4) a method to constrain the
parameters of such unseen companions. These results are enabled by an accurate,
3D, photodynamical model, of a kind expected to become increasingly important
for modeling multi-decade photometric and composite (RV, astrometry) data sets.
