Egypt was part of the Roman Empire which was Christian. Asia Minor (Turkey) was part of the Roman Empire too and therefore Christian. We have already covered that, didn't we?
In the Arabian peninsula you had Arians and Nestorians Christians preaching,
Yes, we have already established that Christians were present in the Arabian peninsula. My point is this: Christianity did not strike deep roots in Arabia and those roots were easily pulled up by Muhammad and his followers. And you disagree with that statement.
while in India you had St. Thomas' Christians right from the 1st century.
Thomas made few converts. Not only were the roots shallow in India, but they were sparse as well. We know that some churches were established even further east in China, but there were few converts. Christianity withered away in China.
Christianity was weak in the East, and it withered away, because it was majority-heretical. A lesson for the Protestants in this.