The plasma membrane of the cell acts as a semi-permeable barrier, regulating what can enter and exit the cell. Only small, nonpolar molecules are able to cross the membrane via diffusion, without the assistance of protein channels. Larger molecules will be blocked, as will molecules that are charged or polar.

This principle is true for both prokaryotic and eukaryotic cells, and is not affected by the presence of a cell wall. Virtually all organic molecules contain carbon and hydrogen; the presence of these atoms will not affect the molecule's ability to cross the membrane.

A hypertonic solution will have a higher solute concentration than the cell. To reach equilibrium, water must flow so that the concentration fo the solution is equal to the concentration of the cell. In order for this to happen, water must enter the solution, diluting it and reducing the concentration. Water will flow out of the cell and into the solution.

Note that the membrane of the cell will prevent ions from crossing.

Homeostasis describes the resistance of the body to change and serves to reinforce equilibrium. Concentration of ions and water in the blood and regulation of body temperature are examples of homeostatic regulation. These processes must be tightly regulated and maintained in order for the body to operate.

Negative feedback reinforces equilibrium and plays a key role in homeostasis. In a negative feedback system, deviations from equilibrium trigger processes that serve to return the body back to equilibrium. In contrast, a positive feedback system will respond to deviations from equilibrium by enhancing the changes, deviating farther and farther from the equilibrium state.

Hormones can play a key role in maintaining homeostasis, but many other molecules also help return the body to equilibrium.

Water can pass through the cell membrane without using energy. We call this passive transport. Diffusion is a type of passive transport and osmosis is specifically the diffusion of water molecules. So all of the answers are correct.

The plasma membrane of the living cell is made up of a phospholipid bilayer, meaning two opposed sheets of phospholipids with their hydrophilic heads facing outwards, and their hydrophobic tails facing one another. This structure allows the cell to remain fluid in shape while also staying "water tight".  

Active transport is the movement of individual small molecules across the plasma membrane against their concentration gradient (from lower concentration to higher concentration). This is usually accomplished by proteins embedded in the membrane which use ATP energy to act as "pumps".

In contrast, osmosis, simple diffusion and facilitated diffusion are all forms of passive transport and do not require additional energy from the cell. These transport methods move with the concentration gradient, rather than against.  

Osmosis is the movement of water across a selectively permeable membrane, like the plasma membrane. It flows with its concentration gradient (from high concentration of water to low concentration of water).

A hypotonic solution is a solution that has a lower solute concentration than the fluid in the interior of the cell (the cytoplasm). When the cell is placed in this solution water will flow into the cell via osmosis, causing it to expand and potentially burst.

A hypertonic solution is a solution that has a higher solute concentration than the fluid in the interior of the cell (the cytoplasm). When the cell is placed in this solution water will flow out of the cell via osmosis, causing it to contract.  

Exocytosis is the transport of waste materials or secretions from the cells. These molecules are packaged in membrane bound vesicles and are released across the membrane to the outside of the cell.