The hypodermis connects the skin to the underlying muscle.

yes, its basically the fatty part of the hypodermis, and then the dermis, which is made up of connective tisse, and then the epidermis which is made up of epithelial cells, stratified squamous keratinized epithelium to be specific.

The stratum corneum is a layer of the epidermis. It is not a layer of the hypodermis.

The hypodermis has two other names: the Subcutaneous layer and the Superficial Fascia

The hypodermis contains connective cells or tissues directly under the skin.