Let me start by answering the final question. Yes, cellular respiration without photosynthesis is possible as long as the oxygen and glucose that cellular respiration requires are supplied via some alternative mechanism.
As the question indicates, photosynthesis and cellular respiration are closely related to each other. The equation for cellular respiration is essentially the equation for photosynthesis backwards.
Photosynthesis occurs within a chloroplast and uses chlorophyll to absorb the light energy that is necessary to fuel the following equation.
carbon dioxide + water → glucose + oxygen
Cellular respiration's equation is the following equation.
glucose + oxygen → carbon dioxide + water
As you can see, the products of photosynthesis are the raw materials for cellular respiration, and cellular respiration's products are the raw materials necessary for photosynthesis.
Cellular respiration occurs in the mitochondria of a cell, and that organelle is often called the powerhouse of the cell. The goal of cellular respiration isn't the production of carbon dioxide and water. The goal of cellular respiration is to use the oxygen and glucose to produce another form of energy called adenosine triphosphate (ATP). ATP is an organic chemical that provides the energy that living organisms need to drive processes within cells and organs. Things like muscle contractions and nerve impulse propagation are dependent on ATP energy.