I have some questions about designer dogs...?

Well the parents were probably a shih tzu/poodle mix and a er/poodle mix. Thats what would make the most sense. Ive never heard of that mix, but the scam artists come out with new stuff all the time. I don't think there is a difference between Chow/GSD mix and GSD/Chow mix, but maybe your right. A Liger means that the mom was a tiger and the father was a lion and a Tigon means the opposite.