Sher,
‘The Ottomans did not make serious attempts to invade Western Europe.’ The Sultan sent an army to take Vienna twice, and failed in 1529 and 1683. So he sends 100,000 soldiers to take Vienna, just for fun. Be serious.
‘In the Roman Empire  .. Turkey.’ If you knew history you would see there was no Turkey then. The Turks were nomads in Central Asia. What is called Turkey now was Asia Minor aka Anatolia. 
‘The increases of population in Europe were of the poor and starving.’ Another fantasy: How can there be an increase in population if the people are starving? Europeans multiplied because of their medical advances. 
‘Same reason no Indians went in the other direction (to Britain) 16th to the 19th centuries.’ Indians did not have the physical means to travel to Britain; no Indian ship knew how to sail to Europe. Indians have flocked to Britain in modern times, illustrating your saying ‘the poor have almost always emigrated (correction, immigrated) to richer countries’.