Interesting reading regarding archeological findings:
http://www.christiananswers.net/q-abr/abr-a027.html
Your third assertion of Israelite archaeological remains not being found in Egypt is true factually, but not necessarily true. Israelite's would have culturally looked liked other Western Asian populations from the Levant. And there are tons of remains of Western Semites in the delta area. So we may actually have lots of Israelite remains without being able to prove they are Hebrews. And the "may" I just used above looks to be very strong. See James Hoffmeier's and Manfred Beitak's work for examples.