Welcome to YT!
As for the skin issues, many people jump the gun and automatically assume it is corn. I would advise you to follow up with your vet and perhaps follow up with a dermatologist. My vet likes to rule out environmental allergies before going with the idea of food allergies. A blood test can help with the environmental allergies, but is not really good for food allergies. For that they do a food elimination diet. She also could have just had fleas and it got out of control. Once they start with the scratching and biting it is difficult to stop.
Luxating patella is indeed very common and many of them live with it without any issues. Just be aware that she can have problems in the future with it. She could end up with a torn cruciate ligament since luxating patella is a knee joint that is slipping and that puts a strain on the ligaments. The surgery can be around $3,000 for one knee. Just so you know.
Collapsing trachea is awful to deal with if it is bad. Sounds like she does not have it and you are just asking. Yes, you should walk her on a harness.
All coats are different. She looks to be pretty and the coat does not look horribly thin. I have found that many pups in rescue come in with coats in ill repair; and that they improve dramatically with good nutrition and grooming.
It is wonderful that you are wanting to rescue...there are so many yorkies in TX looking for homes. They make wonderful companions....they know that someone is saving them and they are so appreciative. I love my little rescues.