The language also split one becoming Avestan and the other Sanskrit. As our prayers are in Avestan language i.e. older Avestan so that was what the spoken language of those times. The Avestan language being also of the same time is put at 1500 BC and the Prophet is also believed to have been around at that time. Gathas also talk about metals, chariots, weapons etc. In 6000 BC the Indo Iranian stock had not yet split.
Different people claim the place of birth of the Prophet in their own home town.
But considering the language of the times, it cannot be western Iran. It would be around North East Iran. The place of birth is put around modern day Kazakhastan. It was an integral part of Iran in olden times. They wanted to kill her so that the people would not turn to Zarathustra for help from their wickedness.