  We reveal the importance of ongoing in-situ star formation in the Brightest
Cluster Galaxy in the massive cool-core CLASH cluster MACS 1931.8-2635 at
z=0.35. Using a multi-wavelength approach, we assess the stellar and warm
ionized medium components, spatially resolved by the VLT-MUSE spectroscopy, and
link them to the molecular gas by incorporating sub-mm ALMA observations. We
measure the fluxes of strong emission lines, allowing us to determine the
physical conditions of the warm ionized gas. The ionized gas flux brightness
peak corresponds to the location of the supermassive black hole and the system
shows a diffuse warm ionized gas tail extending 30 kpc in N-E direction. The
ionized and molecular gas are co-spatial and co-moving, with the gaseous
component in the tail falling inward, providing fuel for star formation and
accretion-powered nuclear activity. The gas is ionized by a mix of star
formation and other energetic processes which give rise to LINER-like emission,
with active galactic nuclei emission dominant only in the BCG core. We measure
a star formation rate of 97 Msun/yr, with its peak at the BCG core. However,
star formation accounts for only 50-60% of the energetics needed to ionize the
warm gas. In situ star formation generated by thermally unstable intracluster
medium cooling and/or dry mergers dominate the stellar mass growth at z<0.5 and
these mechanisms account for the build-up of 20% of the mass of the system. Our
measurements reveal that the most central regions of the BCG contain the lowest
gas phase oxygen abundance, whereas the tail exhibits slightly more elevated
values. The galaxy is a dispersion dominated system, typical for massive,
elliptical galaxies. The gas and stellar kinematics are decoupled, with the
gaseous velocity fields being more closely related to the bulk motions of the
intracluster medium.
