
Hi Mel,
No, there is no stud registry. If people ask if they can use your stud, and the bitch is suitable, and the mating takes place, you sign a Kennel Club official form with the details of your dog, and the date of the mating, and give it to the bitch's owner. It is needed to register the pups with the KC when they are born.
To know if there have been no problems with the individuals in the pedigree, you have to research, research, and research some more. Ask other breeders - you are unlikely to get unbiased information, so ask as many knowledgeable people as you can, and take an average of views! Some of the animals will still be around, maybe being shown. Attend shows and meet them for yourself. Find out about other offspring they have produced, and study them too. Get as many of the books on your breed as you can - there's valuable history and info to be found there. Join a breed club - some of the owners of the dogs may also be members and willing to help. It's a time-consuming thing to do, but absolutely vital if you're going to do it right!