Re: how does epidermis get oxygen when there are no blood vessels?

This is a good question, and relates to the fact that all types of epithelium, including the epithelium lining the intestines (simple columnar epithelium) or the trachea (pseudostratified columnar epithelium) or the skin (stratified squamous epithelium) all lack blood vessels. This is because all epithelial cells manufacture a thin layer of material beneath them called a basal lamina. This basal lamina can't be penetrated by growing capillaries. Normally, a growing capillary can penetrate into other tissues like muscle or connective tissue by secreting enzymes that dissolve extracellular molecules like type I collagen, and thus create little tunnels that they can grow into. Capillary enzymes, however, are for some reason unable to penetrate the basal laminae underneath epithelia.

For most epithelial layers, this is not a problem, because epithelia are generally only 1-2 cells thick. Nutrients and oxygen can easily diffuse into this thin layer of cells. The epithelium covering the skin, however, is much thicker (4-20 layers of cells can be found covering the skin, depending on where in the body you are looking). Thus, the top layers of cells in the skin have no ready access to nutrients or oxygen. Fortunately, cells in the upper layers of the skin are programmed to destroy their organelles, fill up with specific types of a protein called keratin, and die. The dead flakes of skin cells on the surface of the skin form structures like shingles that protect the outer surface of the skin. Hairs are likewise formed from dead skin cells.

A cut that does not penetrate the epidermis will not damage blood vessels, so no blood will leak out and no clot will form. Instead, the skin cells at the margins of the cut will migrate over it to replace the missing cells.

More information about skin cells can be found in an Audio Book I created called "The Building Blocks of Human Life: understanding mature cells and stem cells" which is available in many public libraries. Also, I wrote a more technical book on cells called An Introduction to Cell Biology by JK Young that provides more details about these topics.