According to the problem statement, the only external parameter changing is column pressure. You have to try to understand what the question really intends and where to set the material and energy balance envelope. I interpret the problem question to mean that either the mass flow rate or the mole flow rate of the two products are fixed but they cannot both be fixed if the product composition changes. With those assumptions, your statement 'pressure increase decreases relative volatility making separation more difficult' is the correct approach. Qualitatively, the top and bottom products will be less pure. The question is short and simple but a tricky professor may be trying to set some traps. We do not know what other parameters are allowed to change to keep the balance. Are reboiler and condenser duties fixed? Is reflux ratio fixed? Is there any C component in the overhead product at lower pressure? See the next paragraph for further discussion of this question. All we do know is the tendency of pressure to affect relative volatility. State your assumptions to support your answer and it will show you understand the concepts and should get some credit even if the answer is not what the teacher expects.
Light and heavy key are set by the separation performance requirements of the system. You are not trying to separate component C from component C so it cannot be the light key and the heavy key in the same column. If component A is the light key and component B is the heavy key then there may not be any change in the distribution of component C when the pressure increases. Without more information on product flow rates and component parameters, we just cannot know for sure.