Diffusion and osmosis are both used in order to equalize the concentrations of solutes on both sides of a membrane. This act requires no energy to take place, as solutes will passively flow from regions of high concentration to areas of low concentration. Facilitated diffusion requires a channel protein to allow substances to cross the membrane, but also allows flow down a concentration gradient and does not require energy.

Active transport is needed in order to accumulate solutes on one side of a barrier against their concentration gradient. This requires ATP in order to take place, as the solutes will not flow in this direction naturally.

The cell membrane is composed of a phospholipid bilayer. Polar regions of the membrane face outward and shield a hydrophobic interior. Only certain compounds can cross both regions of the membrane. Polar compounds and ions will be able to interact with the polar regions of the membrane, but be unable to cross the hydrophobic interior. Similarly, large compounds will be unable to fit between the phospholipids. Only small, nonpolar molecules can cross the membrane freely.

Protein channels are placed in the membrane to allow polar and large molecules to cross, further adding to the selective nature of the membrane. Harmful compounds can still enter the cell from time to time, but the selectivity of the membrane helps prevent the potency of these attacks.

A cell wall is a tough, and rigid layer of polysaccharides lying outside of the plasma membrane in plants, some fungi, and some protists. The cell wall provides these cells with structural support and protection. It also prevents over-expansion when water enters the cell. Animal cells lack a cell wall, and only have a plasma membrane.   

The cell membrane controls what enters and leaves the cell. The cell membrane is a selectively permeable phospholipid bi-layer, which admits molecules by passive and active transport into the interior of the cell. The DNA is the genetic code found in the nucleus while cytoplasm is the liquid inside the cell.

The fluid-mosaic model for the cell membrane is a double layer of phospholipids with embedded proteins.  The proteins do active transport in pumping molecules across the membrane.  The phosphates are on the outside and the lipid chains are on the inside of the membrane.

The cell wall provides support and protection for the cell.  Most are made from carbohydrate and protein.  They are not made of phospholipids or lipids.

All these answers are correct and can be used interchangeably, so it's good to be aware of all of them. All cells have a cell membrane, regardless of organism, to separate their internal environment from their external environment. The term plasma membrane refers to the cytoplasm within the cell that the membrane is separating from the external environment. Phospholipid bilayer describes the molecular makeup of the cell membrane as it is composed of a double layer of amphiphilic (something that is both hydrophobic/lipophilic and hydrophilic) phospholipids. Semipermeable membrane refers to the ability of the membrane to allow certain substances cross from one side to the other, while restricting the passage of other substances. Cytomembrane uses the Greek root "cyto", meaning cell, to create a compound word that in the end means the same thing as cell membrane.

Cell membranes are composed of a phospholipid bilayer. Phospholipids have hydrophilic heads and hydrophobic tails. The tails come together to form the hydrophobic inside of the membrane, whereas the hydrophilic heads face the outside of the cell and the inside aqueous cytoplasm. 

Lysosomes are specialized vesicles that bud off of the Golgi apparatus and house digestive enzymes within the cell. Lysosomes have only one outer membrane, made of a phospholipid bilayer, similar to the plasma membrane surrounding the cell.

In contrast, the nucleus, mitochondria, and chloroplasts all have two outer membranes. Each of these is made of a lipid bilayer, for a total of four layers of phospholipids around these structures.

A cell’s cytoskeleton is made up of three types of filaments: microfilaments, intermediate filaments, and microtubules. Microfilaments are made up of actin, whereas microtubules are made up of tubulin. Flagella, cilia, and the mitotic spindle of the cell are made from microtubules. The only filament given that is not made up of tubulin is microfilament.