I am a new Yorkie mom also.. We have a lab mix.
We have the same problems with our little girl Mia. She was born Dec 26, 2008. For the flakiness and the itching my vet put her on Derma caps. You can also find them online. She has been on them for a week now. It is just a capsule of liquid you put on their food. Mia seems to be getting softer every day. For potty training I use pee pads. She had a few spots she likes to go and I always refresh the pads. I own a bissel Green machine and I am bisseling every weekend. Baking soda helps too. Also, For the teary eyes I give Mia Angel Eyes (also online) this really helps with the tear ducts. They can get bacterial infections from being all icky in the eye region. My vet says it's fine to give her. It's just a powder you sprinkle on their food. As far as chewing....Mia loves her water bottles with a couple of inches of water in them. She chases them around the house. Ropes and the little tennis balls that squeek. (we have to hide Shoes, hats and barbies, I don't think any of my daughters barbies have hands or feet)
Hope any of this helps... Good luck.