I'll address your question regarding application of a force to a fixed solid body. Consider a horizontal bar attached to a vertical wall. Suppose you press your hand against the end away from the way. By the nature of the process, the force starts rather quickly from zero and builds up to a maximum within a second or so. The force tends to compress the bar because the far end is fixed. This tends to compress the bar increasingly as the force builds to its maximum. The bar transmits your force along its length and applies it against the wall. The bar is gradually compressed by in proportion to the instantaneous amount of the force. Because of the stiffness of the bar, the compression is very slight. The bar remains under pressure as long as your continue to press on it. The bar has a an elastic modulus, and the amount of compression is the product of the force and the elastic modulus. The latter is known as "Hooke's law", which is valid for both limited amounts of both stretching and compression.

You apply a force whenever you apply pressure against something. If you press twice as hard, you are exerting twice the amount of force.