  (abridged) Gravitationally lensed quasars can be used as powerful
cosmological and astrophysical probes. We can (i) infer the Hubble constant
based on the time-delay technique, (ii) unveil substructures along the l.o.s.
toward distant galaxies, and (iii) compare the shape and the slope of baryons
and dark matter distributions in galaxies. To reach these goals, we need
high-accuracy astrometry and morphology measurements of the lens. In this work,
we first present new astrometry for 11 lenses with measured time delays. Using
MCS deconvolution on NIC2 HST images, we reached an astrometric accuracy of
about 1-2.5 mas and an accurate shape measurement of the lens galaxy. Second,
we combined these measurements with those of 14 other systems to present new
mass models of these lenses. This led to the following results: 1) In 4
double-image quasars, we show that the influence of the lens environment on the
time delay can easily be quantified and modeled, hence putting these lenses
with high priority for time-delay determination. 2) For quadruple-image
quasars, the difficulty often encountered in reproducing the image positions to
milli-arcsec accuracy (astrometric anomaly) is overcome by explicitly including
the nearest visible galaxy in the model. However, one anomalous system
(J1131-1231) does not show any luminous perturber in its vicinity, and three
others (WFI2026-4536, WFI2033-4723, and B2045+265) have problematic modeling.
These 4 systems are the best candidates for a pertubation by a dark matter
substructure. 3) We find a significant correlation between the PA of the light
and of the mass distributions in lensing galaxies. In contrast with other
studies, we find that the ellipticity of the light and of the mass also
correlate well, suggesting that the overall spatial distribution of matter is
not very different from the baryon distribution in the inner \sim 5 kpc of
lensing galaxies.
