Hi Vanessa and welcome to the forum.
Shih Tzu's aren't my breed, but I'd want to know about health, the KC website is a good place to start, but breed clubs often have more information. They are easily googled.
Welcome to the Shih Tzu Club
The KC page indicates there are no health tests they currently recommend for this breed, but some breeders may still test for conditions that occur within the breed overall.
As for questions you need to ask the breeder, I would want to be given the third degree by the breeder as a puppy buyer as well as asking my own questions which would (after asking about health) be along the lines of: the reason why the two dogs were used, what conformation faults/points are they hoping to improve on, what are the temperaments like, has there been any history of illness within the lines they know of, are they shown or have they been assessed for correct conformation, will pups be endorsed/sold under contract/KC registered?
I would have asked a lot of this over the phone before going to see any pups, because once you see pups, your capability for making thought out decisions can fly out the window. So if I were you, I'd suggest asking if you could phone and go through questions before you visit. It's also often the case that you will forget to ask half the questions you meant to because your brain turns to mush when faced with a cute litter of pups. By asking before you go, you can decide if any of what you find out doesn't sit right with you and go from there. I had as many people visit before my bitch had pups as possible, although I had to cancel a couple of visits as she went into labour. I also sent out copies of the contract paperwork, including endorsements and puppy pack so puppy buyers could look through it all and decide if they wanted to go ahead, all of them did thankfully.
Good luck with your search for a pup, and thank you for taking the time to research before you buy your pup, there are far too many who don't unfortunately.
Edited to add, three weeks is quite young to visit pups, I'm not sure if this is an inexperienced breeder, but I'd suggest four weeks minimum, and whatever you do, don't visit more than one litter of pups without a change of clothes. I made people wash their hands and take off shoes before sitting with the pups, to reduce any risk of walked in infections being transferred.