Do small airplanes have AC power? I know that DC power is essential for avionics and that in medium and big airplanes AC (28 V, 400 Hz) is used with DC (28 V). 

Small airplanes have a starter-generator that provides DC, but do they have an inverter too, to provide AC? If yes, then why use AC, and in which systems? And when is AC 26 V used?
I have worked on large and small aircraft.  You will find a 400hz power bus only on large aircraft. The reason is the greater quantity of poles in the generator and hence weight. Smaller aircraft use a 28v DC system for the avionics.