Short answers, pulled from the story.
Sir William Jones delivered the Third Anniversary Discourse to the Asiatic Society in India in 1786. This observation noted systematic correspondences between Sanskrit, Greek, and Latin.
Most linguists agree that Proto-Indo-European was spoken around 3500 BCE before divergence began. Estimates by different authorities can vary by more than a millennium from this timeframe.
The Yamnaya culture emerged on the Pontic-Caspian steppe between 3300 and 2500 BCE. It developed from earlier groups like Khvalynsk and Sredny Stog.
More than 90% of Britain's Neolithic gene pool was replaced by Beaker people around 2600 BCE. These migrants carried roughly 50% Western Steppe Herder ancestry.
Marija Gimbutas formulated her Kurgan hypothesis in the 1950s. It places the Proto-Indo-European homeland between the Dniepr and Ural rivers.