In order to explore these questions, we must first understand the background of the Israelites' stay in Egypt. According to traditional estimates, the people of Israel resided in Egypt for 210 years, and accordingly they became steeped in Egyptian culture. In the book of Ezekiel, God remembers appealing to the people of Israel, "Cast away, every one of you, the detestable things that you are drawn to and do not defile yourselves with the idolatries of Egypt.... But they defied Me and refused to listen to Me" (Ezekiel 20:7-8). The Midrash Rabbah notes that it was very difficult for the Israelites to abandon the Egyptian deities. And so before they could physically leave Egypt, they first had to abandon the Egyptian culture and recognize that they were a nation apart.
Interestingly, this language of separation does not begin until the fourth plague. Ibn Ezra, the classical Bible commentator, concludes from this that the first three plagues--those of blood, frogs, and lice--affected both Egyptians and Israelites indiscriminately. It has been suggested that the first three plagues were specifically directed at undermining Egyptian gods. Egypt worshipped the Nile, a symbol of fertility, which is subverted in the first plague into a bloody symbol of death. The Egyptians had a fertility goddess with the body of a woman and the head of a frog; suddenly, in the second plague, the country is overrun with frogs reproducing at a fantastic rate. The third plague, that of lice, was specifically aimed at the Egyptian cultic elite, because the ordinary commoners were generally covered in lice anyway (from Binah B'Mikrah on Parshat Va'era).Since the Israelites had been worshipping Egypt's gods as well, both the Israelites and the Egyptians were afflicted by these first three plagues.
Beginning with the fourth plague, though, God begins to teach the Israelites of their separate and unique status. This process continues throughout the rest of the plagues, and its climax is the paschal offering. The Egyptians worshipped sheep and considered it an abomination to sacrifice them. In this ultimate act of cultural independence, the Israelites publicly sacrifice the gods of Egypt, and in this way proclaim their own identity. Only when the Israelites realize that they are a separate nation are they able to leave Egypt to pursue their own destiny. It is this birth of national consciousness that we celebrate this Shabbat.