>"I was just wondering first of all if these two products are even compatible with each other?"

Sorry, no.

>"So, what exactly is the pipeline between the two?"

The SX50 doesn't have an external mic input, so there is no "pipeline".

> How do I get the audio from the lapel microphones into the video, into the computer editing software?"

In addition to the above, the link you posted appears to be to just the mic and transmitter, not the receiver, so there's no way that I can see to record any sound from the mic at all.

>"Does this mean that the 'cameraman,' needs to be walking around with a laptop to receive the lavalier microphone audio as well as the camera?"

Laptop? I'm not aware of any laptop that's capable of receiving signals from G-622. Are you saying you have one? If so, that would change things.

Mark