The white cliffs of Dover are so named because they are made of chalk.
Erosion causes it to stay white as white. The Cliffs are made of chalk.
The chalk that forms the White Cliffs of Dover is primarily made up of calcium carbonate from the remains of microscopic marine organisms which lived millions of years ago. Over time, these remains accumulated on the sea floor and were compressed into chalk through geological processes. So, the cliffs are mainly formed from fossils.
Yes, that is why they are called clay cliffs. When it dries, clay is firm, and forms a soft rock, however it is easily eroded, so clay cliffs are often unstable.
Chalk
Because they are made from chalk (calcium carbonate) which is a white material. The truth is that they are really not that white. If you looked closely you would find that some parts are absolutely full of plant growth and flint. The effect that causes them to be "so white" also has to do with reflection of light. The calcium carbonate form coccolith structures that can reflect light. The (south-)western orientation of the cliffs in combination with the rising sun generate the reflection and "light up" the cliffs.
Chalk is a fossil itself and chalk is soft, and so while you might form a fossil; in it, it would not remain. Within chalk there is often harder rock - which sometimes does contain fossils.
Chalk is made up of tiny calcium carbonate skeletons of marine organisms like plankton. When these organisms die and settle at the bottom of the ocean, their skeletons accumulate over time and create thick layers of chalk. As the soft parts of these organisms decay, their hard skeletons become preserved as fossils within the chalk.
Chalk is a hard rock, with large lines of weakness so will erode by physical weathering and the sea.
Yes and so is cliffs
Pastel refers to the colors of the chalk. Pastels are soft colors like baby blue, baby pink and so on. Non-pastel colors are red, blue, green etc.
You will probably need to be more specific about the exact location and time period you mean. However, the "lith" part of "paleolithic" means "rock", so it was probably made from a type of rock that can be worked to form a sharp edge, such as flint. In which case they would most likely have found flint nodules on the shore near chalk cliffs; flint occurs in chalk, and wave action can wear away the much softer chalk leaving the flint nodules strewn about the base of the cliff.