a) We often distinguish between the marginal product of labor and of capital. They are defined as

MPL = Δq/ΔL

MPK = Δq/ΔK

MPL answers the question "if we increase the input with one unit of labor, by how much does the production increase?" MPK is the  corresponding measure if one increases the input with one unit of capital.

b) The law of diminishing marginal returns states that if one increases, say, labor input by more and more units, then eventually one reaches a point where additional units increases production by fewer and fewer units. For example, because of congestion in the factory.

This law is not a result from economic theory but partly an empirical result and partly based on speculation.