Does it make sense to open one window all the way when the other window is much smaller? I can't wrap my head around this idea because I don't know much about air flows.
Say we have this imaginary apartment with two windows, one of which is two times smaller than the other:

Will the first one let more air through than the second? Or is it the same because of the smallest window?

How does this work? 
 A: If you are familiar with electric circuits in a quite loose analogy you can look at your windows as impedances for the air current. Since current is turbulent (take a look at the Reynolds number if you do not know it) the air does not directly go all the way down through all the windows, but each of them will create some impedance to the flow. The bigger the window the less the impedance so yes, fully open also the second one! You will also get more diffusion which is not included in the previous discussion.
A: Each window represents a restriction to the air flow. The greater the pressure difference across the aperture, the greater the flow.
An electrical analogy: each window is a resistor. The current through the resistor is proportional to the voltage across it - but when you have two resistors in series they must carry the same current (air that enters through one window must exit through the other). If the total voltage across the two resistors is constant (the "force of the wind"), then if one resistor is smaller (the "big window") it leaves more of the voltage available across the second resistor (the "small window") - thus the over all air flow will be greater. See this diagram:

So yes - it makes sense to open the larger window fully. The pressure drop across it will be smaller, the pressure drop across the small window will be larger, and there will be more air flow through the apartment.
