You had the settling of people in the "fertile crescent" which could be divided into Phoenicia, Assyria, and Mesopotamia. Though I have seen maps where it appears Mesopotamia was split into Akkad and Sumer at one point in time. Then Sargon of Akkad conquered and united Akkad, Sumer, and part of Assyria into the Akkadian Empire (missing anything?). Was this then the end of major events in Mesopotamia or was there more?

Okay, where to start? I guess at the beginning. "Mesopotamia" is a greek term meaning "between two rivers" or some such, and is generally synonymous with "the fertile crescent" in ancient contexts, describing an area focused on the long winding arc of the Euphrates and Tigris rivers - from southern Anatolia, curving past the feet of several mountain ranges in what is now Iraq, and emptying south across broad plains and marshland into the Persian Gulf. Assyria is the more northerly portion of this area, while Sumer and Akkad inhabited the lower regions. Sumerians were the earliest urban force in Mesopotamia, with cities like Ur, Lagash, and Uruk. They spoke a language unrelated to other linguistic groups on record, and invented writing in the form of ideographic cuneiform around the 3rd millennium BCE. Akkadians were a semitic-speaking population located to the north of Sumer who came to dominate the local geopolitics, culminating in Sargon's conquest and unification of numerous cities into an encompassing kingdom in the 23rd and 22nd centuries BCE. In many ways, this was the beginning of large-scale geopolitical events in the fertile crescent, not the end. The history of the kingdoms and empires that would come to occupy this cradle of civilization is vast, and stretches several millennia. I'm writing this off-the-cuff without my notes or books, so I can't go into detail (hopefully someone like /u/farquier will come along for that), but I can give a basic outline. Sargon's kingdom collapsed after about two centuries due to pressure from revolts in the Sumerian south and an invasion by the unsettled Gutians from the Zagros mountains. The Guti rule was overthrown by Sumerian kings after 50 - 100 years, which resulted in a span of Sumerian resurgence known as the Ur III period. It was characterized by various city's kings gaining temporary control over their neighbors through the fortunes of war and diplomacy, before being dispossessed in turn.

During the 2nd millenium, Akkadian gradually displaced Sumerian as the primary spoken language, and new ethnic groups were integrated into the growing urban cultures. This period gave rise to the Old Assyrian empire in the hilly north, and Babylonia in Sumer-Akkad. Assyria being somewhat earlier, Babylonia initially emerged in the 19th century BCE as a regional insurrection against the impositions of their northern counter-parts, and other neighboring kingdoms like Elam.

Man... this stuff is complicated to recall, and I'm losing focus already. I'm giving up for now, hope that was at all helpful.

Did all of these places share the same basic religious ideas and origin stories for their societies? More specifically did Sumeria use the same origin story as Mesopotamia?

First off, Mesopotamia refers to a broad group of cultures, of which Sumer is one of the earliest. Mesopotamian religions did share a general pattern of pantheistic worship centered on temple bureaucracies, even borrowing gods and rituals from neighbors and predecessors, but there were significant distinctions. While large elements of Sumerian religion were adopted by Babylonians, including the templates of major gods and myths, it was common to appropriate these elements for the aggrandizement of a new contemporary deity of local importance, like the insertion of Marduk (the prime deity of Babylon) into an essentially Sumerian origin story in the form of the Enuma Elish. Other gods, like Inanna/Ishtar, were shared in alternate forms by many different pantheons over time. Ishtar may have even been part of the basis for the much later Greco-Roman goddess, Aphrodite/Venus.

Was this then the end of major events in Mesopotamia or was there more?

So your question is really big, because the problem is that the history of Mesopotamia is a very, very long one. There where many, many empires over time and sometimes city that had multible empires. Just so you understand, how long this history is, the first city go back to 3800 BC and over all these thousends of years we can more or less track history.

So first I would ask, what time period do you care about? Its impossible in my answer to go threw every city and empire.

Im not a expert on the Akkadian Empire so im not gone answer for these events specificly but the are not the first major events, nor the last major events in Mesopotamia.

Did all of these places share the same basic religious ideas and origin stories for their societies?

Again, since we are tracking such a long time period, this question is difficulte. There are some major trends religion or otherwise that can be seen quite often, but most cultures also put there own spin on things. Sometimes we just dont know what there religion was like.

Mesopotamian political history after the Akkadian Empire(and before!) is a long and complicated affair, and there are still some lacunae in our understanding. Since I can't possibly fit it all into one Reddit post, I would first suggest you look at Michael Roaf's Cultural Atlas of Mesopotamia and the Ancient Near East. It's a fantastic overview of what's where in Mesopotamia and clarifies a lot of the smaller regions and the major states in them at any one time. Incidentally, one thing that may help some of your confusion is that you seem to be using Mesopotamia to refer to Babylonia(roughly from the Persian Gulf to a little north of Baghdad), which is more normally treated as the southern half of Mesopotamia along with Assyria in the north(roughy corresponding to modern northern Iraq and Iraqi Kurdistan-in fact, modern Mosul and Erbil are both on or near the site of the major Assyrian cities of Nineveh and Arbela).