Is Shenyang safe for young girls, like 21 as my daugher is going there in January?

Yes, Don't worry about your daughter. China is a very safe country, despite what you might have read. I feel more comfortable downtown at night here than I would in Toronto.

I have been in China for 7 years and have never heard of any physical violence against foreigners here in Shenyang or anywhere else in Liaoning Province - I don't know about the others. But I would say that your daughter will be safe. She will easily make friends with other girls her age and maybe boys too, all of whom will be happy to know her and help her. A society, like China's, that is basically homogenous is more harmonious.