Does this mean that since they are so aligned they could show heterozygosity and then a disease causing gene would be recessive?

No, it just says that your reads were mapped almost all of them (95.69% as properly paired) and a few ones has issues: singletons = only one pair mapped correctly, secondary alignments = some reads have a second good match, duplicates = some reads seems to be duplicated (same sequence and quality scores)

To answer your question you need to check where are they aligned, coverages, SNPs, etc.