If you study the genomes of the populations of Europe as well as parts of Central and South Asia, you can reconstruct a very broad family tree rooted in a shared genetic ancestry from in a population who lived somewhere in Eurasia at a certain point in time. If you also study the languages of those same populations, you can independently reconstruct a family tree of languages that culminates in the reconstructed Proto-Indo-European language that would have existed at the same point in time. The simplest explanation for this is the spread of Indo-European-speaking populations, and not merely the language itself, from a single ancestral population.
David Reich is aggressive about these genetics results though. IIRC I read a NYT story once where he came in and claimed to have upended all of Polynesian history based on the genetics of a few historical skulls they found, but it didn't seem like strong enough evidence to me.
Primarily the male population. Genetically much higher proportion of the female population survived.
Of course that’s an exaggeration as well. In much of Southern Europe and other areas the replacement was far from full.
Laryngeals replaced by vowel lengthenings, merging of consonsants, vowel shifting based on other sounds, etc. It's like there were many different events where "Indo-European with a heavy foreign accent" suddenly emerged.
This is absolutely true.