I agree with Nicola.
Lots of young pups are picked up as having heart murmurs and they do grow out of them, most fairly quickly. Having a heart murmur is not a reason for a dog not having papers, thats a separate issue, they may be lost, he may never have been registered by the breeder are most likely reasons. Anyone who buys a pup has the same anxieties as you and we all head to the vets for a check up. Most check ups include vet looking in eyes, ears, mouth for problems, feeling pups legs and how good his movements are so highlighting joint problems, checking their genitals and bottoms and listening to their heart and lungs, which I've no doubt is what your vet did for your pup. If you have not considered insurance then now is a good time to get him insured as it will mean less worries financially should there be problems with him in the future, if he isn't already insured then the heart murmur will be excluded for the time being, but usually if he has been heart murmur free for 12 mths then it will then be covered.
No one will be sick of your questions, you are trying to do the best for your dog.
As for full investigations to check for other problems, if your vet does a thorough check then consider him fit and enjoy him whilst you can, but that goes for us all.
Hope this helps.