The new sample of giant radio sources II. Update of optical counterparts, further spectroscopy of identified faint host galaxies, high-frequency radio maps, and polarisation properties of the sources

Our sample of giant radio-source candidates, published in Paper I, is updated and supplemented with further radio and optical data. In this paper we present: (i) newly detected host galaxies, their photometric magnitude, and redshift estimate for the sample sources not identified yet, (ii) optical spectra and spectroscopic redshift for the host galaxies fainter than about R approximate to 18.5 mag taken with the Apache Point Observatory 3.5 m telescope, and (iii) the VLA 4.9 GHz total-intensity and polarised-intensity radio maps of the sample members. In a few cases they reveal extremely faint radio cores undetected before, which confirm the previously uncertain optical identifications. The radio maps are analysed and the polarisation properties of the sample sources summarised. A comparison of our updated sample with three samples published by other authors implies that all these four samples probe the same part of the population of extragalactic radio sources. There is no significant difference between the distributions of intrinsic size and radio power among these samples. The median redshift of 0.38 +/- 0.07 in our sample is the highest among the corresponding values in the four samples, indicating that the angular size and flux-density limits in our sample, lower than those for the other three samples, result in effective detections of more distant, giant-size galaxies compared to those detected in the other samples. This sample and a comparison sample of normal-size radio galaxies will be used in Paper III (this volume) to investigate of a number of trends and correlations in the entire data.