In which meiotic division does the separation of the homologous occur? What are the ploidies of the generated cells after the end of that process?
The separation of the homologous chromosomes happens in the first division of meiosis, or meiosis I. After the end of this cell division two haploid cells are made, each having dissimilar chromosomes (with no set of homologous). Note that in the cells generated after meiosis I each chromosome is still duplicated as the homologous chromosomes and not the identical chromatids were separated.
Cell Division Review - Image Diversity: meiosis I