If Digit is drinking a lot of water and peeing a lot it sounds like hyperthyroidism. He is likely to have an over active thyroid gland. I am taking Jack to the vets tomorrow to have one of his thyroid glands removed as he has been diagnosed with it just last week.
From the symptoms it sounds almost identical, the losing weight but still having and appetite and bringing up furballs sound exactly the same. Jack pulls his fur out all the time due to hyper active behaviour so brings it back up, sounds the same for digit.
Be sure to get him checked out as my vet told me just last week if it's left, because they have an increased and rapid heart beat it can cause an enlarged heart and this is dangerous and makes it harder to treat, an enlarged heart can also lead to other things like kidney failure and disease.
I'd definately get him checked over, and mention hyperthyroidism to the vets and also mention EVERY symptom, the weight loss, the vomiting etc. They'll know straight away as my vet said as soon as I told her he was losing weight it was his thryoid as it was very swollen.

I hope you find out what it is and if Digit can be sorted out Good Luck