How does the ancient human DNA tests and Haplogroups work?

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I remember reading that DNA half life is around 521 years and every 1000 years it’s loosing 75% of it’s viability. So anything over 1000 years is iffy.

I also remember there are over 3 billion gene base pairs in human DNA. So, how come scientists can be sure that what they are looking is human DNA and how can they differentiate between human ancestors? How reliable and correct these tests for the ancient human DNA? When there are over 3 billion base pairs but the most they can find is 100 to 300 pairs mostly in ancient human DNA.

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