1) First of all, it wasn't the Red Sea. The actual Hebrew expression referred to a reedy body of a water, likely the Bitter Lakes in Egypt.
2) The idea that the sea was "parted" is a rather late version of the story, and one likely influenced by the Chaoskampf myth (cf. especially Isaiah 51:9-10 which directly relates the two together). The older verison of the story in the Song of the Sea (Exodus 15) does not claim that the waters were divided; they instead were heaped up and piled together, as if they were dammed up.
3) The story is not that the Jews were slaves in Egypt because they had done anything wrong. They were slaves because a new king arose who did not know of the Jews' privilege with the former pharaoh.
4) There was a guy thirty years ago who suggested that a tsunami caused the miracle at the sea. His idea has not been accepted by historians and scholars, and it is geologically improbable. Moreover, the event thought to have caused the tsunami (the eruption of Santorini) probably did not occur at any of times suggested to have been the time of the Exodus.
Did it really happen?
Maybe. It's hard to tell. Some scholars take the early date of the Song of the Sea (determined by linguistic and stylistic evidence) as evidence of the historicity of the exodus. But this is rejected by many others, since the poem mentions things dating centuries later (such as the Temple in Exodus 15:17), so even tho it is early, it is not early enough. The narrative is even later, but appears to have details that fit well with the Nineteenth Dynasty (especially ch. 1 and 5), tho even these could be recalled or known later (and employed to embellish a fictional story). It should be recalled that Israel and Judah had people in the population whose ancestors left Eygpt in the Hyksos expulsion, others who were POWs pressed into slavery, and the land as a whole was under Eygptian control for centuries before Israel came into existence. So I have no doubt that some memories of a sojourn in Egypt and an escape from Egypt may ultimately have germs of historical basis, but my opinion is that the exodus story as a whole is a nationalistic legend that integrates memories and tales about two or three hundred years of oppression and individual exodus events, and which posits a single unifying event that explains how the nation came into existence.
