I know that there may be some controversy when it comes to the Exodus and the Hebrews as slaves in Egypt. Are there any historical/anthropological evidence of this?
What about the history of the Hebrews after leaving Egypt? How much of it is completely true, how much is exaggerated, and how much seems to be completely false?
First of all, the Old Testament is not a history textbook. The Historical parts of it are written with the intent to compare each king and their deeds to the prophesied King (the Messiah). Also, most of the actual written documents of the Bible that we have are themselves from time periods much later than the actual events.
However, many persons and places in Old Testament history have been corroborated.
We have no records of any person in the Old Testament before King David. There just was no writing in that area of the world, and all the other external people mentioned in the Pentateuch were either not mentioned by name (e.g. Pharaoh) or we do not have a record of their name in extrabiblical sources.
However, we do have records from Iron Age Israel that mention the House of David (referring to the southern Kingdom of Judah, which was ruled by David's descendants). These include the Tel Dan Stele and the Mesha Stele.
We also have extrabiblical references to other kings of Israel, including King Omri (Mesha Stele again), King Jehu (the Black Obelisk of Shalmaneser III).
A seal was found in Jerusalem bearing the name of a scribe called Baruch the son of Neriah, who was the scribe who wrote the book of Jeremiah (according to the book of Jeremiah).
Many extrabiblical kings have also been confirmed, including several of the kings of Aram (such as Ben-Hadad and Hazael), Nebuchadnezzar, etc.
We even have a record of Cyrus the Great sending captured people back to their homelands after the conquest of Babylon (which would include the sending back of the Israelites).
Basically, the books of Kings and Chronicles are the historical records of the kingdoms of Israel and Judah. However, it must be acknowledged that they are written after the fact, and are to be treated the same as other historical documents from the same period. They were written with a particular agenda in mind, and some events may be embellished to show a point. In addition, the earlier you go, the less we have in terms of archaeological corroboration.
As for your specifics regarding the Exodus, we have no direct evidence of the Israelites in Egypt or of the Plagues or the Israelites leaving. We do, however, have evidence of people from the Levant area living in Lower Egypt.These sites include Tel el Dab'a (also known as the Hyksos capital city of Avaris, from the time when the "Asiatics" ruled Egypt, though "Asiatics" were living there for some time by the time this happened), Izbet Helmi, Tell el-Mashkuta, Tell el-Retaba, and others in this region. There are also inscriptions and paintings of "Asiatics" coming into Egypt from the Beni Hassan tombs. Therefore, Semitic peoples were absolutely present in Egypt during the time when the Exodus story took place (by Semitic peoples, I mean people from the Land of Canaan, outside Egypt, foreigners from northeast of Egypt). We do not, however, have any records of Israelites specifically in Egypt (though we really shouldn't expect to), since they really weren't a people group until after the Exodus. We also don't have anything concrete regarding the Exodus from the Egyptian perspective. We have archaeological sites from the period corresponding to the Way of Horus mentioned in the Bible, but scholars are divided about whether the Exodus should be dated to ~1240 BC or to ~1440 BC, and therefore there is no agreement about which Pharaoh is mentioned in the biblical text.
It should not be surprising that the Egyptians did not record this event, as it probably did not reflect well on the government at the time, and Egypt was notorious for censoring their own history to remove everything negative that happened.
For a comprehensive overview of the Old Testament and various archaeological corroborations and discrepancies, you should check out
Grabbe, L. L. (2007). Ancient Israel: What do we know and how do we know it?. London: T & T Clark
This is an excellent, comprehensive chronological overview of the entire Old Testament, incorporating archaeological evidence to establish exactly what we know and do not know about the history of the Old Testament. It is a fantastic book.
hi! hopefully someone will drop by to fill in any blanks (especially re your last question.. I'm not sure whether there have been posts on that), but you can get started on a couple of sections of the FAQ