I would first like to define some terms first based on the permeability.
Impermeable: A membrane that does not allow any substance to pass through it is called an impermeable membrane. e.g. Cuticle layer
Permeable: A membrane that allows the free passage of substances through it is called a permeable membrane. e.g. Primary cell wall
Semi permeable: Semi permeable membranes allow the movement of most substances if they are small enough by osmosis or diffusion. It does not require any energy or in other words uses passive transport. e.g. Egg membrane
Selectively permeable: As the name suggests these membranes are more selective and the substance that can pass through are limited. Substances that cannot pass through by passive transport is transported by active transport through integral proteins embedded in the cell membrane.
Though the cell membrane acts semi-permeable to the small oxygen and carbon dioxide molecules it is best to call the cell membranes as selectively permeable membrane because of the degree of the control they have over on what to allow and not to. Try reading this page for the difference between semi permeable and selectively permeable.
You were right in saying that the cell membrane allows the free movement of water but controls the movement of other solute particles according to its needs. If the molecules are small enough and they are non-polar, they can easily diffuse inside. If they are polar , like water and glucose, it is difficult to push their way through the non-polar tails of the phospholipid bilayer. The channel proteins will aid in the movement of such substances through passive transport. The channel protein that allows the rapid flow of water through is called an aquaporin. If the substances need to move against the concentration gradient, from a lower concentration to a higher concentration, they use energy and pass through the proteins. This is active transport e.g. Sodium potassium pump.
And for the last question, diffusion is the net movement of substance from a region of higher concentration to a region of lower concentration. Note that this happens along the concentration gradient and does not need any energy. The cell cannot exactly "control" that movement. If the particle is small enough and the polarity is right, it can pass along the gradient. Movement of $CO_2$ out of the cell and movement of $O_2$ inside the cell is by diffusion.
Correct me if I went wrong somewhere.