What is the blood relationship between a half-brother and a child born to an aunt and nephew? DNA detected their relationship?

Strictly speaking, everyone's DNA is different, because there are gene mutations and recombination, which are individual differences. The genetic difference between half-brothers and sisters is greater than that between them and their aunts and nephews. If you want to know the difference in detail, you can do microsatellite DNA paternity or simply compare it with mtDNA (cytb or COI gene). It's simple. Generally only a few bases apart, there can be no big difference.