Trying to understand refrigeration through statistical mechanics (i.e. what happens to each molecule), as you are trying here is going to be a bit tricky. Refrigeration is really best explained by classical thermodynamics, using properties of the fluid like enthalpy, pressure, entropy, etc. which themselves can be understood using statistical mechanics. As a matter of fact, the vapor-compression cycle was invented before Boltzmann's theory.

Two significant mistakes in your diagram:

• after the expansion valve, the droplets are not floating in "free space". They are in an environment where the pressure is low enough that they can vaporize, but this is still in the continuum regime. There are plenty of refrigerant molecules around, the system is a vapor+liquid saturated equilibrium. (It is also best to understand that the valve enforces the low pressure by restricting the flow of refrigerant, rather than the compressor creating it, in a causal sense, but that's mostly nitpicking) 
• the refrigerant droplets vaporize completely because of heat transfer from the outside in the evaporator, not vaporizing THEN absorbing heat from the outside. That's the crux that makes the vapor-compression cycle so efficient: the heat is transferred from the outside to the refrigerant and from the refrigerant to the outside during phase changes (evaporation and condensation) at constant temperature.

My advice for understanding the vapor-compression cycle:

1. vaporizing a liquid requires a lot of energy (the enthalpy of vaporization). At constant pressure, this energy can be provided as heat, like boiling a pot of water (the stove provides energy).
2. Symmetrically, condensing a gas releases the same amount of energy, which at constant pressure is provided as heat, like water condensing on a cold mirror.
3. The boiling point of a substance varies as a function of pressure: at low pressure, the boiling point is low, at high pressure, the boiling point is high.
4. Refrigeration consists in vaporizing a liquid at low pressure, hereby sucking a lot of energy from the environment at cold temperature, and then condensing this same vapor back into a liquid at high pressure, therefore releasing the same amount of energy (plus compressor waste heat and other inefficiencies) into the environment at a higher temperature.

The compressor and the valve are there to enforce this pressure differential between the hot side and the cold side.

In terms of looks would look better as a cycle (like in circle or some rounded square). It would also be conceptually closer to what is happening, as the actual mechanism is a cycle.