What is the methodogy used to determine the exact genetic flow from one area to another and the times in which it flowed?
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Having just read A Short History of Humanity by Krause and Trappe, the argument seems to be as follows:
You calculate a "distance" (i.e. probably some useful metric) between the genomes e.g. of individual ancient and modern Central Asians and individusl ancient and modern Indians. Then there is probably some aggregation (clustering/averaging?). If the distance between ancient Central Asians and ancient Indians is considerably greater than between ancient Central Asians and modern Indians, the conclusion is that modern Indians have a considerable amount of (ancient) Central Asian ancestors.
You can do this if you assume that there is a constant mutation rate and that a great part of the human genome does not yield any evolutionary advantage and is only random noise (the authors claim that 50% of the human genome is just useless noise)
The authors of the book mentioned above are mainly dealing with Europe and are applying this argument not only to "ancient" remains and modern humans, but to remains from different ages. E.g. it seems to make quite a difference if your ancient Western European remains are 10000 or 6000 or 3500 years old.
Re. your question 2: The book notes that there is a considerable genetic difference between European human remains that are older respectively younger than roughly 4800 years. They conclude that this is because of a major migration wave from Eastern Europe (apparently the difference between older Eastern European remains and younger Western European remains is smaller). They note this fits well with various archeological evidence. I think the argument for migration into India could look similar.
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