I think that fat is called "marbling".
steak
A thin piece of wood?
Cheese, bread, wine, perhaps some sliced beef and a piece of fruit.
A thin piece of wood is called a "slat."
fibrous connective meat
carpaccio
A piece of paper or thin piece of metal will provide protection from?
NOT a thin piece of something
it is very thin
Thomas Edison was a thin man throughout his life.
A thin pointed piece of metal is commonly referred to as a "point" or "pointed end." These can be found on various objects such as nails, needles, or awls and are typically used for piercing or puncturing materials.
A paillard is a slice of meat which is pounded thin and grilled.