Yes the Gutians/Mitanni/Kassites, Mannaeans were absorbed by Medes. Cyrus literally equates Western Media with Gutium and Heredotus doesn't even make a differentiation between the Mitanni and Medes.
Yes the Persians absorbed the Elamites and even went as far as taking Elamites costumes and absorbed Elamite elements into their language too.
The South Indian in South Iraq having Elamite origin is absolute bollocks and the believe that they came from South Asia is also very outdated. If that was the case you would find even higher levels of South Indian in Persians of Fars. but they don't have higher levels to other Persians or these Iraqi samples.
If anything the proto Elamites must had been very Iranian Neolithic.
South Iraq has been known as a hotspot for exotic ancestry in modern times. They did have some people from Africa and India settle there as Sailors due to trade. Also there are quite a number of Iraqis and Kuwaitis with Baluchi origin settled in Central and South Iraq due to religious reasons. So it is no suprise to find Iraqis with higher Indian DNA. They are not necessary Gypsies either.
https://en.wikipedia.org/wiki/Afro-Iraqis
https://en.wikipedia.org/wiki/Muzaffar_Al-Nawab
Mais Gomar for example has partially South Asian origin.