A breeder provided the pedigree for the dog I'm considering. How can I research the longevity/heath issues for the dogs in the pedigree?

Not really sure what you are asking exactly, but one way to know about the important aspects of your pups family line, like whether the parents, grand parents and so on had testing done for eyes, HD and such, is to look on the pedigree itself, I believe most breeders list those certifications and when they were tested and cleared, directly next to the name and birthdate. Mine are like that. In past Huskies I've had, I did searches.from names in their pedigree for something different (I was basically looking for littermates of mine) and I believe it was a site called PawVillage that also had pedigree, pics, status of championship, and such turn up as results after typing in the name of the dog, which also stated things like whether they were tested for HD/cataracts, etc.

AKC can do a search for you that will include any health stuff they have, but much like a carfax they will only be as good as the breeders were about actually keeping them up-to-date (so take into consideration how reputable your breeder really is before committing to using AKC because they charge). A good breeder should have all the health information back several generations on hand themselves that they would and should use when deciding on pairing for litters. This stuff should be included with the paperwork you would get when doing the registration on your dog through AKC.

I have an AKC issued pedigree but not sure how to lookup by registration number or DNA number on AKC website.