Water will move towards the side the containing solution A. Solution A has a higher concentration of solutes so it is hypertonic to solution B and water will always move from a hypotonic solution towards a hypertonic solution even if the hypotonic solution has more types of solutes in it. The types of solutes is irrelevant for this case, only concentration of solutes matters. Remember: water follows solutes.

The cell will take in water and most likely burst, killing the cell. When a cell is placed in a solution hypotonic to it, water will flow from the hypotonic surroundings into the hypertonic cell. This causes the cell to grow with water intake until it bursts like a water balloon.   

Facilitated diffusion is the type of passive transport that relies on transport proteins embedded in the cell membrane. No energy is used in this transport since the molecules follow their concentration gradients so it is not active transport. Osmosis refers to passive movement of water only.   

Sodium-potassium pumps are an example of membrane proteins that undergo active transport. They function by using ATP for energy to pump potassium and sodium against their respective concentration gradients. Specifically, two molecules of sodium is pumped out of the cell for every three molecules of potassium pumped into the cell. The sodium-potassium pump is of monumental importance to all animals that use it, and it is often the target of lethal injection since even slightly altering its function is always fatal. Passive transport does not use energy. Both facilitated diffusion and osmosis are examples of passive transport.  

Endocytosis is the process by which the cell takes in macromolecules by creating new vesicles from the cell's plasma membrane. Phagocytosis, pinocytosis, and receptor-mediated endocytosis are all different types of endocytosis.  

In facilitated diffusion, molecules, such as glucose move through protein channels from an area of higher concentration to an area of lower concentration.  It is not active transport, using energy. Movement of molecules through the cell membrane without use of a protein is known as simple diffusion; osmosis is a type of simple diffusion.

Endocytosis occurs when the cell engulfs an external substance and takes it into the cell by the infolding of the cell membrane.  Exocytosis occurs when the cell secretes a substance outside the cell.

The glycolipids on the outside of the cell are made of proteins and carbohydrates.  Proteins result from translation from DNA to RNA, and they are modified in the Golgi apparatus to form glycoproteins.  "Glyco" refers to sugars, which are carbohydrates.  Lipids are fat molecules that are not often used in cell signaling, but rather as stored energy sources.

In exocytosis the membrane of a vacuole surrounding some material fuses with the cell membrane, forcing the contents out of the cell wall.  The substance is secreted out of the cell.  The process by which foreign matter is engulfed by immune cells is phagocytosis. Water and salts are stored in the sarcoplasmic reticulum in certain cell types (muscle) but this is not exocytosis, which involves the removal/expulsion of substances from the cell into the extracellular environment.

In order for a material to be transported across the cell membrane, against its concentration gradient, energy is required. For example, the sodium-potassium pump hydrolyzes one molecule of ATP to pump 3 sodium ions out of the cell and 2 potassium ions into the cell. Since the potassium levels are much higher inside the cell than outside, energy is required. This is known as active transport.