(a) False - Surface skin cells are continuously lost and replaced by the underlying cells.
(b) True - All types of human cells, have 46 chromosomes. The only type of cell which does not have 46 chromosomes are the sex cells, which have only half of the number, so they have 23 chromosomes. The egg cell is a sex cell (found in female). So it must have 23 chromosomes.
(c) False - Nuclear membrane disappears in Prophase itself, however it reappears during Telophase.
(d) True - Mitotic cell division can be a mode of asexual reproduction in unicellular organisms like amoeba or yeast cell which divides into two daughter cells.
(e) True - While the maternal and paternal chromosomes are separating, the chromatid material gets exchanged between the two members of a homologous pair resulting in genetic recombination.