Well, to be honest, I don't know how to start... I guess the fundamentals. A transistor is not quite exactly like a controllable resistor, because it is not linear in the characteristics (voltage/current relationship is not like a resistor's).
To avoid writing a whole book worth text here, I would ask you to look at for example
https://www.electronics-radio.com/a...-does-a-transistors-works-basics-tutorial.php
In addition, I would say very briefly a few words to your numbered questions:
1. Yes, you have to provide all power from outside, and then some more - because some (often large) part will be lost as heat. And regarding biasing: Yes. You need to have a correct "operating point".
2. The input power source is used to power the amplifier components. Usually DC is used - and the audio output is AC. The amplifier is generating the output AC power from the DC power, and is controlled by the input signal (which defines waveform, frequency, and amplitude of the output AC)
3. The output power is larger - either because both voltage and current are larger, or at least one of those is larger. Depending on amplifier type and application, the voltage and current amplifications vary a lot!