Typically chinchillas with serious health problems act depressed, especially those with liver disease. I'm not sure you have that much to worry about. Like I've said most cases of fur chewing that get posted on our board are from harmless or treatable causes. An overall unhealthy appearance is concerning though. The good news is that a number of curable things can explain it too including diet.
As far as your questions Oatmeal should be unsweetened, plain oatmeal. Cheerios are okay. I'd say no more than 4-6 rings in a day.
Rose hips are kind of rare but sometimes you can find them in online stores that cater to exotic pet owners. I recommend not giving any treats until after his diet is straightened out and after you get a vet exam and after he's not been stressed and only if his fecal output is normal. Interaction without treats can go a long way with chinchillas. (Yeah, that's a lot of ANDs.)...
I also recommend weighing your pet once a week routinely. There will be variations as he gets less treats and goes on a better diet. Having a good baseline healthy weight is an handy diagnostic tool. Typically weight loss of 15% or more indicates something needs to get checked out.