1) Is there any merit to the thoughts that breeding different breeds together will produce genetically stronger animals - i.e. eliminating a lot of the very unfortunate illness being bred in purebred lines today
No, not unless both parents have been health tested/screened and cleared against all genetic defects common to that breed. Plus only dogs who have been titled and proven to be impeccable examples of that breed should reproduce.
The "hybrid vigour" you are talking about does not apply here, since all dogs are the same species.
No one who has a titled and health tested purebred would consider cross breeding it, so that leaves the unhealth tested and untitled dogs to produce the designer mixes and puppies could very well end up with genetic defects common to BOTH breeds.
Millions of mixed breed dogs die every year. I see no logic in choosing to pay big bucks for deliberately produced mutts when there are so many to choose from at shelters and rescues.