The potential energy increases as the substance goes through phase changes. Therefore the potential energy is highest at the last possible instant of the most energy intensive phase change. In this case it is at the end of segment 4.

Because phase changes happen when the kinetic energy (temperature) remains constant melting will occur during a flat portion of the heating curve.

In this case it is the first flat portion because solid is the lowest energy phase represented in this diagram. Therefore the melting point is at .

This question is presenting us with a scenario in which heat is being added to a block of ice at its melting temperature. It's asking us to identify a false statement.

Recall that when anything goes through a phase change, the temperature remains the same until the phase change is complete. Furthermore, since temperature is a measure of the average kinetic energy of a system, this will not change either. Moreover, as energy is added to a system, the bonds between the components of that system will gradually weaken and then break as the entropy of that system increases.

Definition of triple point: where solid, liquid, and gas exist in equilibrium

the critical point is where the solid and gas cannot be distinguished

The point detailed in the question is the triple point of water on the phase diagram. At the triple point all three phases of a chemical coexist; as such the correct answer is solid, liquid, and gas. 

A physical change is a process where the physical properties of a substance are changed.  Here water undergoes a phase change from the more disordered liquid state to the more ordered solid state, which is indeed a physical change.  A chemical change describes when a substance undergoes a change in the identity of its constituent molecules.  Here although the water has gone from the liquid phase to the solid phase it is still composed only of water molecules so a chemical change has not occured.  Entropy describes the degree to which a system is ordered.  Here we do have a change in entropy becasue the liquid water was more disordered than the solid water. 

This is a description of condensation from the gas phase to the liquid phase, then freezing from the liquid phase to the solid phase.

At a pressure of one atmosphere, carbon dioxide can only exist in the solid phase or the gaseous phase. Solid carbon dioxide will sublimate at standard conditions.

Raising the temperature will simply make the carbon dioxide sublimate at a faster rate. In order to allow the solid carbon dioxide to melt into the liquid phase, the carbon dioxide must be subjected to a greater amount of pressure. This will shift equilibrium away from the gaseous state and toward the liquid state.

Whenever you see a problem like this, immediately draw a mental point on the phase diagram to establish your starting conditions. In our case, the conditions fall in the range of the liquid phase of the water. This allows us to eliminate some of our answer options.

Next, determine what change is occuring and on which axis the change is occuring. We are decreasing pressure, so you are going to need to move down on the y-axis towards 0. Draw an imaginary line from the initial point to where the final point should be. In our case, the final pressure is extremely small. This point is not on the y-axis, but we can use our inference/inductive skills to determine that we will pass through the solid phase (ice) as we approach the gas phase (water vapor). Even if you didn't know the water would become vaporized, based on the graph you knew that the liquid phase had to be followed by the solid phase, and only one answer choice has that option.