Tough one. That issue with Lizzy not backing off, personally I would of let Zoe do her thing there. Lizzy has to learn/respect where the boarder goes.
As for fighting, Gizmo is getting his fair share at the dog park. But even with Dobermans, and Rotwielers, they don't go for the kill. They just try to wrestle the other do the ground and hold him there so he understands. Gizmo has been shoved to the ground several times…haha, it's so funny...actually he is on the ground every time. I think his ego is bruised.
The seriousness you can hear in the growls I was told at my puppy class, and it seems to be correct. You can hear the bass/darkness of the growl change. If it gets very very deep that's a sign of it going to seriousness. Also the way they bite. If they bit/jab, that's okay, but if they bite and start to shake (like with toys) that's a "kill".
But I am far from an expert.