  HD95086 (A8V, 17Myr) hosts a rare planetary system for which a multi-belt
debris disk and a giant planet of 4-5MJup have been directly imaged. Our study
aims to characterize the physical and orbital properties of HD95086b, search
for additional planets at short and wide orbits and image the cold outer debris
belt in scattered light. We used HARPS at the ESO 3.6m telescope to monitor the
radial velocity of HD95086 over 2 years and investigate the existence of giant
planets at less than 3au orbital distance. With the IRDIS dual-band imager and
the IFS integral field spectrograph of SPHERE at VLT, we imaged the faint
circumstellar environment beyond 10au at six epochs between 2015 and 2017. We
do not detect additional giant planets around HD95086. We identified the nature
(bound companion or background contaminant) of all point-like sources detected
in the IRDIS field of view. None of them correspond to the ones recently
discovered near the edge of the cold outer belt by ALMA. HD95086b is resolved
for the first time in J-band with IFS. Its near-infrared spectral energy
distribution is well fitted by a few dusty and/or young L7-L9 dwarf spectral
templates. The extremely red 1-4um spectral distribution is typical of
low-gravity objects at the L/T spectral type transition. The planet's orbital
motion is resolved between January 2015 and May 2017. Together with past NaCo
measurements properly re-calibrated, our orbital fitting solutions favor a
retrograde low to moderate-eccentricity orbit e=0.2 (0.0 to 0.5), with a
semi-major axis 52au corresponding to orbital periods of 288$ yrs and an
inclination that peaks at i = 141deg, which is compatible with a planet-disk
coplanar configuration. Finally, we report the detection in polarimetric
differential imaging of the cold outer debris belt between 100 and 300au,
consistent in radial extent with recent ALMA 1.3mm resolved observations.
