What operations during preflight and pre-takeoff engine run-up cause a change in engine rpm?
You will get a change in engine speed doing a mag check, cycling the carburetor heat, if equipped, and cycling the propeller governor.  You will also see a drop in oil pressure and a rise in manifold pressure when cycling the propeller governor as well.

The reasons?  

Carburetor heat increases temperature of the mixture passing through the carburetor, thereby decreasing its density.  Consequently, as the same amount of fuel is being metered into the air steam in the Venturi throat as before, this causes the mixture to become richer and the engine to produce less power and run slower than before.  

Mag checks involve turning off individual magnetos, causing the combustion in the cylinders to become less uniform, resulting in a power loss and slower engine speeds.  

Cycling the propeller governor causes the governor to slow the engine by increasing the angle of attack of the propeller blades.  This creates a greater workload on the engine.  Lower engine speeds also cause the engine driven oil pump to turn slower, decreasing the oil pressure. And, as manifold pressure measures the pressure of the intake air at the cylinder head, an increase in the workload increases the air pressure at the manifold, causing the spike in indicated manifold pressure with the prop governor set to its lowest speed setting.

Cowl flaps are simply moveable panels which can alter the flow of cooling air around the engine to better maintain engine cooling at low speeds when ram air flow through the cowling is limited.  I’ve never heard of a situation where cowl flap position causes an engine to run slower or faster, though the cylinder head temperatures will change quite a bit and there is a risk of overheating and damaging an engine if you are running at high power settings at low air speeds for extended periods.