Ahhh, the mess that is 21MTC. A decoder manufacturer invented it; the NMRA decided they knew better and changed it and IIRC changed back to the European standard for it. Anyway, one thing you'll need to be careful of is, is the motherboard designed for fully amplified outputs (aux 3, 4, 5 and 6) or logic level outputs for aux 3, 4, 5 and 6.
Other than that, to address the questions, if you not going to use an input then I wouldn't bother hooking that wire up. As for the ground, there's no telling how that's utilised on the motherboard without tracing it out. You may be much better off not hooking the negative from the LM to the breakout board and just connecting straight to the keepalive.
- Tim