Audio over ethernet is only available currently in a dante configuration, with additional hardware and software needed.
In your current environment there appear to be 2 options. Firewire is one, and you can configure the mac to use the digital return on the mixer, keeping all inputs free. A good option for this would be to load itunes on the mac, and use itunes remote on the ipad for music control via wifi. Second option would be a series of cables, adapters to run from the headphone jack on the computer to the rca connectors on the mixer. A firewire connection as long as you mention may not work. Runs of that long are not supported, so you are on your own to get it to work.