For the Solid-State amplifiers, I have written an overview about the classes and working principles:
Output transformers could be used in a solid state amp, is uncommon though. In tube amps, you often need an output transformer in order to power low impedance headphones or speakers.
One thing about power I want to look into is how much that changes depending on how “complex” the signal is. In other words: 1kHz sine is power x, but what power is 100Hz, 1kHz and 10kHz playing at the same time?