Hi!
Welcome!
First off let me just say, thank you for doing research and being dedicated to only buying from a reputable breeder or rescue. You can find a lot of info in the Health & Breeder sections too.
Is there such thing as a teacup size dog?
There is no such thing as a teacup. The breed standard size is from 4 - 7 lbs. However, purebred Yorkies
do come in all different sizes. The term 'teacup' is used to entice uneducated buyers into paying more for something they are lead to believe is 'rare'.
Do teacups (or the smaller Yorkies) pass on sooner
I've never heard that they pass on any quicker, but I do believe they have a higher chance of having medical conditions that may contribute to a shorter life span.
What are the warning signs of a bad breeder?
There are many, some of the most obvious is using the terms, teacup or rare over and over on their websites. Advertising that they breed multiple breeds of dogs, large number of puppies always available, not allowing you to come to their home to see the parents and puppies, etc.
I have also seen the smaller Yorkies have much worse health conditions that require constant trips to the vet and they are overall more sickly. Is this true?
Again, I think that medical conditions in the extremely small Yorkies may lead to their health struggles. You have to realize how these extremely small ones come about. It can come by irrepatable breeders inbreeding to focus on the 1 trait of 'size' or breeding dogs that shouldn't be simply because the are small.
I don't think that size alone indicates the health of the dog, but it can be a factor if improper breeding was used to obtain that size.
Please anyone, correct me if I've said something wrong as I am also learning about this wonderful breed.
The AKC website has a list of breeders. That would be a good place to start. There are also several on this site that you could contact too, just check in some of the other sections.
Good luck in your search. Keep asking questions and be sure to keep us updated on your progress!!