Mustang, the pre-amp, among other things, amplifies the incoming voltage from a player or other source device up to a level where when it's combined with the additional amplification that the amplifier does, the voltage is high enough to drive the speakers at a loud level. The pre-amp typically amplifies the voltage by 12dB or a bit more, which is 4 times, while the amplifier amplifies about 29dB, or 30 times. Besides some amplification, the pre-amp also processes the incoming signals for such things as digital to analog conversion, bass management, etc. Because of the processing function they're also referred to as pre-amp/processors or pre-pros.
To connect the receiver(which has both a pre-pro and an amplifier inside)to a separate amplifier you use regular coaxial cables from the pre-amplifier outputs(pre-outs)on the back of the receiver to the inputs on the amplifier. The separate amplifier then is entirely responsible for powering the speakers to which it's connected, while the amplifier channels in the receiver which were previously used for that just idle.
Yes, with suitable player outputs and receiver inputs, the HDMI cable is just connected to the HDMI input on the receiver.
