Are breeds like this prone to health problems or can you expect them to live a normal amount of time.
Unanswerable question. You don't know what's going to happen when they cross. Could get the best of both or the worst of both. One of my Gordon's died at the age of 6 from a rupture lung. No injury, it just let go. Average life span of a Gordon is 10 years or so. My bloodhound lived to 9. Average live expectancy is 4-6 years (although the reputable breeders are working on longevity). Dogs are like cars-you can get a lemon at any time.