I couldn't see the pics but if you have any doubt, taking them to the vet is the best way to go. Sometimes too much dust can make their skin dry out so 3 times a week is good for dust. Does the spot smell? Sometimes they will wet in their dust and roll in it, if you don't catch it...but that also looks and smells similar to a fungus so it's better to be safe than sorry with that and have a vet check it out. Is the spot growing? Mine did that once and the vet said it was best that I did bring him in because without seeing it, he couldn't tell me over the phone...it turns out it was just him wetting in his dust and I didn't catch it. He only did that once, thankfully. The other thing, in response to possible chewing...I've had some trouble with my little guy with that too. He gets separation anxiety and I had to be away for a family emergency.
Now, he travels with me and he's much happier. (Most chins would not like to travel but mine seems to find it more stressful to be left home without me, than to travel. He travels great and it's cheaper than the vet bills and the stress on all of us to get him better!) Chins will sometimes chew for multiple reasons, normally some sort of stress. (could be the change of scene, food, lots of different things) Mine has only done it when I've been away from him for a period of time so it was easy to pin point the problem. Honestly, if you're worried about anything and being that he's a new one to you, it wouldn't be a bad idea to take him in to get checked over and a physical. That way you find out anything you need to know that might be a problem and get a better answer as to what's going on with him. Look for a good exotic vet in the area. You'll want to have him established with one anyway because, trust me, things can happen fast with a chin and you'll want to know where you could get him in fast if need be. They're wonderful and fun but something I've learned is that it's always a good idea to have a vet on hand so that if you need one, even to ask questions, you can find one. Because of the chewing with separation anxiety thing my little one went through, I've gotten to know our vet pretty well and he knows Nipper.
As far as refusing to chew on certain things...is he eating and drinking normally? It's very important that if they stop eating and drinking normally or seem like they're less active. I describe it as the "wounded animal defense" because they are prey animals and to show injury by nature would make them a target so they hide pain and things well. If they start doing anything like that...they need to see a vet ASAP. At the same time, chins have their own tastes of what they like. My sister-in-law that had one that refused to chew on any wood chews that didn't have bark on them. Nipper isn't really choosy with his chews but he goes through phases of favorites. He's never had anything with bark though. He likes lava rocks but then he'll go through phases where he'll prefer something else. I keep a variety around for him. His current favorite seems to be little wood chews that are in the shapes of fruit because he can pick them up and run with them.
The other thing that could cause fur to come out is a "fur slip" if you are holding him when he does it or something is scaring him (which is easy to do with a new baby in a new environment), they shed fur sometimes as a defense mechanism. The idea being that they can slip away from a predator.
Read lots and lots any chance you get to familiarize yourself with chins and their care and needs. It's well worth it to stay as educated as you can. I also find it really fun to learn about them. They're fascinating little critters. Also, as you get to know your little one and bond with him, you'll find that he has his own way of communicating with you that is really fun. Congrats on being a new chin owner! (Sorry if this is a bit of a book.)