Your questions are not only difficult (in the sense that it is difficult to give precise answers to them), they also demand presentation of a whole lot of background data, which cannot be done here. What we recommend you to do is to get to the library of the university nearest to your home, go to the sections dealing with biblical studies and Jewish history, and start reading. A comprehensive work on Jewish history from its beginnings to the end of the Middle Ages is Salo W. Baron, A Social and Religious History of the Jews (1952-1983), but its treatment of the biblical period is rather cursory and outdated. For this period, as a textbook to begin with we would recommend J. M. Miller and J. H. Hayes, A History of Ancient Israel and Judah (1986, 2nd edition 2006). In any event, we should note that in historical studies there is a considerable difference of opinion among scholars on many issues, with different theories proposed to explain the same facts, so we advise you to “beware the man of only one book” (as said by Thomas Aquinas), to read as many different views as you can, and to figure out for yourself what appears most reasonable.
In the way of answering your questions, we can note that it is usually impossible to pinpoint the specific persons who became the progenitors of any given human population, ancient Israelites included. The stories of the Patriarchs are taken in current biblical scholarship as lacking historical value, not so much because there is no extra-biblical evidence for Abraham, Isaac, Jacob or his twelve sons (the chances of finding ancient sources relating to a specific non-royal family are slim anyway), but because the historical details appearing in the biblical sources themselves point to the background of the period later than 1200 BCE – which is too late for the Patriarchs by any biblical chronology. The details in question are, e.g., the mentions of Philistines and Arameans in the book of Genesis, or the mention of the “Ur of the Chaldeans.” The one thing that we can tell for sure is that the people of Israel are mentioned in an inscription of the pharaoh Merneptah, dating from c. 1208 BCE, and they are mentioned in the geographical context of Canaan. In fact, there are some scholars who dispute the connection between the Israel mentioned by Merneptah and the Israel known from the Bible, but their arguments are not persuasive.
Belief in the Exodus from Egypt is shared by all (or almost all) biblical sources, which, as far as the current scholarship is able to tell, were composed over a period of several centuries (starting from somewhere between 1200 and 700 BCE and ending somewhere about 400-300 BCE, if we leave aside the book of Daniel) and in different social and ideological circles. This appears to imply that belief in the Exodus from Egypt was shared by almost all the Israelite society (or at least, by the literate circles in that society), and originated quite early. On the other hand, archaeological finds from the area of the Israelite settlement in Canaan display no connection between the area’s inhabitants and Egypt. The material culture of the archaeological sites in the area of the Israelite settlement is a rather poor variety of the Canaanite material culture. So, here we have a problem. Perhaps there was a small group of people who had left Egypt, blended with the part of the Canaanite population known as Israel, and their traditions of escape from Egypt eventually became shared by the whole Israelite population. Or perhaps the biblical mentions of the escape from Egypt are a vague recollection of escape from the sphere of Egyptian rule in Canaan (the kings of Egypt did rule Canaan in the 15th-12th centuries BCE, but their rule was never strong in the highlands of modern Samaria, which was the main area of the Israelite settlement, and after c. 1200 BCE the Egyptian presence in the highlands was hardly existent). But these are admittedly mere conjecture, which at the present time can be neither proved nor disproved.
Concerning the belief in one god (YHWH), dating its origin depends on dating the different biblical sources, which is sometimes a problematic issue. One should also make a distinction between worshipping YHWH alone and believing that he is the supreme deity, while allowing that other peoples are entitled to worship other entities (as expressed, e.g., in Deuteronomy 4:19-20; according to current biblical scholarship, the book of Deuteronomy was probably composed in the 7th century BCE), and the belief that YHWH is the only deity in existence, so that worshipping anything else is senseless, even for gentiles (as claimed time and again in Isaiah 40-66, the part of the book of Isaiah that was written in the late 6th century BCE, according to biblical scholars).
In any event, it should be pointed out that the mainstream historical tradition shared by the Jews during the Second Temple period (539 BCE-70 CE) held the Jews of that period to be descendants of the exiles from the First Temple-period kingdom of Judah (destroyed by the Babylonians in 586 BCE), while other people were allowed to enter the Jewish community through adoption of the Jewish religion and way of life. Newcomers of the latter kind were especially common during the Hasmonean and the early Roman periods (from 164 BCE to 70 CE), and it is a moot question when the formal act of conversion became necessary for a non-Jew to be considered a Jew.
The theory about Khazarian origin of the Ashkenazi Jews appears to lack historical corroboration, and it is generally assumed that the Jewish communities in late medieval Eastern Europe were established mainly by migrants from the Western Europe, where, in turn, Jewish communities were established during the early Middle Ages (before c. 1000 CE) by Jews migrating from the shores of the Mediterranean. But it appears that during the social and religious transformations in Western Europe between c. 400 and c. 800 CE (the period during which the conversion of the peoples of Western Europe to Christianity took place), a considerable number of pagan Europeans had also joined Jewish communities. So no person living today and considering himself a Jew can be reasonably sure that his ancestors two thousand years ago were also Jews – which is the same situation as with any other human population.
And of course, until a relatively short time ago (approximately the 19th century, although dates vary according to the specific region involved), all people – not only Jews – were religious, in the sense that they believed in some deity, and the worship of that deity played a central role in their lives, both private and social. During the last 200 years or so, the role played by religion in people’s lives within the realm of Western civilization has been diminishing, and Jewish secularism is only a part of this process.