I would thaw it out. I know some big dog people feed frozen to slow down gulpers, but it sounds like with the shivering that thawed would be more comfortable for them. You can do raw meaty bones a couple times a week for dental health and recreation.
Not sure on the tear stains. I know it can be a problem across for the board for most chi's. If food hasn't changed, I would tend to think it might be environmental? Pollen or something which is causing the eyes to water more than usual? Some people have had success with adding just a bit of apple cider vinegar (with the mother) to the water dish.
Baseline blood work would be fine. I have blood drawn once a year when I do a heartworm test, just to keep a close eye and catch any changes. Tell them you want a CBC (complete blood panel) with electrolytes and thyroid. That should catch anything going on. Some vets call it pre-op bloodwork but you want the more extensive test, not just liver and kidney function.
BUN can sometimes be elevated in raw fed dogs. All the bloodwork lab values have been developed off of kibble fed dogs, so there may be slight differences. Here's an article you can read and print off for your vet if anything comes back abnormal ...
Anytime I've had a dog start acting "off" it has been due to pain. Either a disc problem or some sort of soreness. Dogs are great at hiding pain, but they may act 'sad or depressed' and so that angle should be thoroughly looked at by your vet.