Gene flow Puns

For example, I take the instance of Central Asian migration into India.

Say geneticists studied

a) ancient bones in C.A

b) ancient bones in India

c) living people in Central Asia

d) living people in India.

Case 1: -

Say they found a particular haplogroup (A) which is present only in Central Asians, and another one (B), which is present in Indians (both living people, aka options c and d). Then they also found another haplogroup (C), which is present in both individuals.

Question 1: - How do they then determine that it was the Central Asians who migrated and not Indians? Is it due to coupling this evidence with other sorts of evidence like general climate/vegetation? Or is it due to the fact that progressively, unique genes found in Central Asians decline in quantity when moving north to south, and the unique Indian genes aren't found outside India at all (Indus Valley genes)? And if I am not wrong, Indus Valley civilization people were descended from Africans who migrated via Yemen/Oman and the historical Elamites were their cousins, so even the so-called unique Indian gene can be found outside India...how do they then describe the direction of the gene flow?

Case 2:- Say the ancient bones of Central Asia (dated to 3000 BC) showed some genes which were common between ancient bones found in India (dated to 1500 BC).

Question 2: - Does this lead to the conclusion that the migration was from CA to India, latest by 1600-1500 BC? Is there any other technique to find the timing of the gene flow?

Question 3: - Modern ancestry tests have several obscure ancient groups like Neolithic Iranian farmers, Oriental Hunter-Gatherers, BMAC etc. Are all of these from bones taken in specific areas like Zagros Mountains (for iranic hg), Central Asia and Bactria (Afghanistan)? And these bones were dated to the specific time periods when these proposed civilizations were also historically dated?

Overall, I want to understand the nuance of the genetic tests which offhandedly say, that "XYZ" group migrated to "PQR" location in "ABC" era without giving the details.