Is the epidermis continuously being replaced through cell reproduction involving meiosis?
No, it is actually mitosis by which new cells are created by the germinative region of the epidermis.
The germinative layer or deepest region of the of the epidermis is filled with rich new cells created by mitosis. These cells are constantly pushed upwards as new cells are produced for Replacement of old cells, repair of damaged cells and growth of the tissue.
The cells then push upward into the middle layer of the epidermis which can be referred to as the layer of dying cells. In this layer cells lose up to 90% of their water content and are filled with keratin as they harden and die. Melanocytes produce melanin which sets in the cells and provides the skin with color.
The cells continue upwards into the cornfield layer of flat dead cells which form an outer protective barrier to the outside world. These cells are constantly peeled away as we watch, put clothes on and take clothes off, scratch etc.... These cells actually become the majority of dust in our homes.