Okay, I just had a look at the User's Guide for the WK-7600, and there is an "Accompaniment MIDI Out" function (see page E-133), so I assume you'll need to turn that on if you want to record the auto accompaniment.
It looks like you can also turn each of the keyboard's 32 parts on or off with a "Part On/Off" function (see page E-43), so you might also need to turn on the specific parts you want to record.
The 32 parts are described on page E-36; they're divided into parts A01 through A16 for the keyboard, song sequencer system track, metronome, and auto accompaniment, and parts B01 through B16 for the 16 channels of the song sequencer, MIDI file playback, or received MIDI data. But that doesn't necessarily mean that the keyboard can transmit all 32 parts using two MIDI ports (as some keyboards can do); I think it's still limited to transmitting and receiving 16 channels on one MIDI In port and one MIDI Out port.
Also, you might need to look at the other settings for each part, such as volume and pan (see page E-43).
The pages which look like they might possibly be relevant are E-36, E-43, E-133, E-143, E-145, and E-161.
As far as the DAW, what you might want to do is set up a project with 16 MIDI tracks, and assign each one to a specific MIDI channel of the WK-7600 (i.e., track 1 = channel 1, etc.), and then save the project as a template before you actually record anything, so you can start with the template whenever you want to record the keyboard rather than having to set up all the tracks each time. Don't worry about any tracks that won't be needed for a specific project, because you can always delete any tracks that you end up not recording to.
By the way, the Cubase function that I mentioned, for separating each MIDI channel to its own track, is called "Dissolve Part." You shouldn't need to worry about that if you create and save a template for yourself, but you might want to use it after importing a MIDI file into Cubase.
One other issue you might run into has to do with capturing all the settings for the various channels. Normally a keyboard will transmit settings as they're changed-- e.g., if you select a particular tone then the keyboard will transmit the Bank Select and Program Change values which correspond to that tone. If you set up the keyboard's tones and other parameters before you start to record in the DAW, those settings won't get captured because they've already been transmitted.
Some keyboards have a function that will send the data for all of the settings at once, sort of like a "bulk dump," so you can record them. On my Yamahas this function is called "Initial Send," but I didn't check to see if the WK-7600 has a similar function.
If not, one thing you could try is to get everything set up on the keyboard and then save the settings to a Registration Memory. When you're ready to start recording in your DAW, you can start recording, then recall the Registration, and hopefully the keyboard will transmit the MIDI data for all of the saved settings at that time so you can capture them. Otherwise you might end up with a lot of Note On/Off events but no Bank Select, Program Change, and other Control Change events (i.e., Reverb Depth, Chorus Depth, Channel Volume, Pan, etc.), such that when you play back the recorded data from the DAW to the keyboard it sounds like everything was recorded using the GM1 Grand Piano tone!
The worst case scenario would be that you need to manually insert Bank Select, Program Change, and other Control Change events at the beginning of each track/channel in the DAW.