As for it being mythology parading as history or vice versa, I wouldn't be as clear cut either. The archaeological record sticks close to the biblical narrative until a precise point in time, the start of the Omrid dinasty in the northern kingdom of Israel and the foundation of Samaria. From that point onwards, the biblical narrative is corroborated (in its general guidelines) both by the archaeological record and by historical records of non-Israelite peoples (the steles of Moab and Ben-Hadad of Damascus, or the Assyrian records). But from that point backwards, we have only the biblical narrative itself. All the events reported in the OT older than the middle of the VIII century BC can only be studied by analyzing the text of the Bible itself. I wouldn't call that history, but rather mythology. The closer in time the biblical narrative gets to the VIII-VII centuries BC, the more historical it becomes, with less mythical elements.
Reliance on a single written source is not unusual. And for this time period, that is more than you can normally hope for. That doesn't make it automatically history, but that does not mean it should be discarded.
If not for the Bible's religious impact, this wouldn't even be a question. It would be definitely a source used by historians, as much as any other for the era. Indeed, a very productive source, so much more detailed than contemporary parallels.
On a technical point, do you distinguish between myth and legend? And would you then rather that we refer to the Exodus as legend? I didn't make the distinction before (and to make it worse, I also used national myth for a complex of interwoven mythical, legendary and historical stories) but I agree there is a difference between Genesis, where YHW appears as an actor in the story, and Kings etc., which reads as a history book and in which He takes a back seat. However, there is a shades in between those poles. Joshua reads as history but is flatly contradicted by archeology. Exodus doesn't read as history, it's a miracle-filled story centered on a hero. For a Roman comparison, I'd go with Virgilius' Aeneas rather than Livy.
They are not really comparable. Virgil's Aeneid is a coherent literary work by a poet. Exodus is a mess of clippings by a hurried editor.
The story of Aeneas is, of course, not due to Virgil. It is much older e.g. Livy sets it down "as certain fact", even while he acknowledges there are divergent narratives of the arrival of the Trojan emigrants.
The editor of Exodus is approaching it more like Livy than Virgil. He is not showing off literary skill or consciously fantasizing for heroic effect. He is trying to compile multiple divergent accounts of a historical event, maintained by legends, which he believes is a fact.
The editor of Exodus does a poorer job than Livy. Livy actually tries to be coherent, imposes his own narrative and acknowledges divergent sources when they arise. The Exodus editor just cuts and pastes without warning, which is why we end up with pointless repetitions and inconsistencies.
Admittedly, there is more myth and miracles in Exodus then there is in Livy. But that seems the fault of the original narratives, and how they were originally written, not something added by the editor of Exodus for a grand overarching Virgilesque goal.
No, that just means these older sources shared an earlier myth. It says nothing about the historicity. (furthermore of course, we don't have access to these earlier sources)
It says more than that, particularly when we can detect the differences between accounts.
Suppose you knew nothing of, say, WWII, and read a single American book about it and no other. Its historicity would be dubious. But suppose instead your single book was an anthology, with various chapters, containing narratives from various sources, some American, some British, some Soviet. Would your confidence in the historicity of the event be higher or just the same as a single American book?