Welcome to YT!
My Mandie's hair tends to curl some and I think it is because she was shaved before. It seems that gradually, as it grows, it doesn't curl as much. It does still a little though. Maybe this is what's going on with Annie.
To clean her face, I usually use a wash cloth and warm water daily (to clean the eye goop and such) and then I use baby shampoo when it really needs washing. I wet her face and rinse it with a wash cloth so the water doesn't get up her nose or anything like that.
You say Buddy has wiry hair and that he is registered? Is he AKC registered? I ask because wiry hair is not typical on a yorkie. They usually have silky or cotton coats.
Post pics of your babies when you can. We love pics!