Gas flows in and out of galaxies through their circumgalactic medium (CGM) are poorly constrained and direct observations of this faint, diffuse medium remain challenging. We use a sample of five $z$ $sim$ 1-2 galaxy counterparts to Damped Lyman-$alpha$ Absorbers (DLAs) to combine data on cold gas, metals and stellar content of the same galaxies. We present new HST/WFC3 imaging of these fields in 3-5 broadband filters and characterise the stellar properties of the host galaxies. By fitting the spectral energy distribution, we measure their stellar masses to be in the range of log($M_*$/$text{M}_{odot}$) $sim$ 9.1$-$10.7. Combining these with IFU observations, we find a large spread of baryon fractions inside the host galaxies, between 7 and 100 percent. Similarly, we find gas fractions between 3 and 56 percent. Given their star formation rates, these objects lie on the expected main sequence of galaxies. Emission line metallicities indicate they are consistent with the mass-metallicity relation for DLAs. We also report an apparent anti-correlation between the stellar masses and $N$(HI), which could be due to a dust bias effect or lower column density systems tracing more massive galaxies. We present new ALMA observations of one of the targets leading to a molecular gas mass of log($M_{rm mol}$/$text{M}_{odot}$) < 9.89. We also investigate the morphology of the DLA counterparts and find that most of the galaxies show a clumpy structure and suggest ongoing tidal interaction. Thanks to our high spatial resolution HST data, we gain new insights in the structural complexity of the CGM.
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