The area called the gooch in slang terms is called the perineum in medical terms.
It is generally called the "groin".Iguinal
Iliac is the medical term meaning area around the hipbone.
The groove between the nose and the upper lip is called the philtrum.
It is called an ulcer
The area below the ribs is usually called the abdomen. It may also be the flank or upper quadrant.
The caudal area is the medical term meaning tail region, although in humans it may be called the coccygeal region. Cauda means tail, and coccyx is tailbone.
Mastitis is the medical term meaning inflammation of the breast.
It's the area in front of the elbow
A blackened area of skin, usually resulting from a burn, is called an eschar. Eschar is removed during debridement, as it is devitalized tissue.
keratosis
The most common terms would be nasal and oral, but depending on the specific area, there are many terms that would be used.
Melanodermatitis or postinflammatory hyperpigmentation are terms meaning an excess of melanin in an area of skin inflammation.