  Debris disks are the intrinsic by-products of the star and planet formation
processes. Most likely due to instrumental limitations and their natural
faintness, little is known about debris disks around low-mass stars, especially
when it comes to spatially resolved observations. We present new VLT/SPHERE
IRDIS Dual-Polarization Imaging (DPI) observations in which we detect the dust
ring around the M2 spectral type star TWA\,7. Combined with additional Angular
Differential Imaging observations we aim at a fine characterization of the
debris disk and setting constraints on the presence of low-mass planets. We
model the SPHERE DPI observations and constrain the location of the small dust
grains, as well as the spectral energy distribution of the debris disk, using
the results inferred from the observations, and perform simple N-body
simulations. We find that the dust density distribution peaks at 25 au, with a
very shallow outer power-law slope, and that the disk has an inclination of 13
degrees with a position angle of 90 degrees East of North. We also report low
signal-to-noise detections of an outer belt at a distance of ~52 au from the
star, of a spiral arm in the Southern side of the star, and of a possible dusty
clump at 3.9 au. These findings seem to persist over timescales of at least a
year. Using the intensity images, we do not detect any planets in the close
vicinity of the star, but the sensitivity reaches Jovian planet mass upper
limits. We find that the SED is best reproduced with an inner disk at 7 au and
another belt at 25 au. We report the detections of several unexpected features
in the disk around TWA\,7. A yet undetected 100 M$_\oplus$ planet with a
semi-major axis at 20-30 au could possibly explain the outer belt as well as
the spiral arm. We conclude that stellar winds are unlikely to be responsible
for the spiral arm.
