My name is ***** ***** I’ve been involved professionally with dogs in the health and behavioral fields for over 18 years. It will be my pleasure to work with you today. I answered on the other page as well.
The most common cause for a dog to urinate blood is a urinary tract infection. If the pup has been treated and is no longer urinating blood, then it shouldn't be a problem. If you can get a release from the rescue in order to talk the their vet , then that might be something you can do to ensure you don't get a pup that has an ongoing issue. But without getting an exam from a disinterested third party, there really isn't any way to be sure.
There is a genetic disorder found in great pyrenees dogs called Glanzmann’s thrombasthenia (GT). Read more on this here:
The fact that multiple pups had bleeding would concern me. I really can't make the decision on whether you should adopt the pup or not, but I'd be inclined not to given the fact that multiple pups had bleeding.
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Since there have been recalls on certain foods, please check the following site to be sure the food your animals eat is not affected. If it is affected, contact your vet as soon as possible. Have your dog seen if they have any symptoms.