That is correct. Asia started to develop around 3000 BC. The first organized civilization began around 2000 BC. But if you want play that card... The Nile Valley was originally inhabited around 10000 BC. Agricultural organization and building began around 6000 BC. The states were finally united into a 2 kingdoms around 3500 BC. The period of the pharoahs began around 3300 BC and the kingdoms were brought together. Mesopotamia began to be inhabited and farmed around 6000 BC. Summarian civilization began around 4000 BC.
DNA anthropolgy has traced the origins of Homo Sapien existance to a region of central africa. And as the population grew humans spead first in North Africa and then Mesopotamia and Asia Minor. My anthro professor required everyone to watch the National Geographic documentary, "The Origin of Man". Very interesting film.
And as far as your third paragraph above. Todays problems in the middle east are definitely rooted thousands of years ago. One word: Religion.
Ancient Egypt under went many changes between monothesism and polytheism. And also underwent many civil wars.
In anacient mesopotamia the religion was polytheistic. The Assyrians and Babylonians fought over a chief diety when there was a movement to monotheism after Hammurabi influence. Assyrians believed in Assur and the Babylonians believed in Marduk. Assyrians eventually conquered Babylonnia and destroyed the statue of Marduk.
And this doesn't even touch the religious conflicts that arose (and are still present) with the rise of Judaism, Christianity and Islam. Religious turmoil has plagued the region since it was first culturalized. This is the underlying cause.
I will say that the Roman Conquests involved mostly "Europe". But to say that it didn't great affect the middle east is a lie. And take a look at the Greco-Macedonia empire. It barely even makes it west of the Adriatic. It completely involved Asia Minor and the Middle East with the Persians. You can't use "Europe" very losely. When "Europe" is discussed it normally refers to the wester portions during and after the Roman Empire.