The country of Sodom borders upon [Lake Asphaltitis]. It was of old a most happy land, both for the fruits it bore and the riches of its cities, although it be now all burnt up. It is related how, for the impiety of its inhabitants, it was burnt by lightning; in consequence of which there are still the remainders of that Divine fire, and the traces [or shadows] of the five cities are still to be seen, as well as the ashes growing in their fruits; which fruits have a colour as if they were fit to be eaten, but if you pluck them with your hands, they dissolve into smoke and ashes. And thus what is related of this land of Sodom hath these marks of credibility which our very sight affords us.
This sounds like something from Sir John de Mandeville, but I've actually seen this fruit growing near the Dead Sea. It's called a Sodom apple, and looks vaguely apple-shaped from the outside, but if you open it up, it's like dandelions seeds inside.
About missiles from Roman catapults, Josephus writes (V.6):
The stones that were cast were of the weight of a talent, and were carried two furlongs and further. The blow they gave was no way to be sustained, not only by those that stood first in the way, but by those that were beyond them for a great space. As for the Jews, they at first watched the coming of the stone, for it was of a white color, and could therefore not only be perceived by the great noise it made, but could be seen also before it came by its brightness; accordingly the watchmen that sat upon the towers gave them notice when the engine was let go, and the stone came from it, and cried out aloud, in their own country language, THE STONE COMETH so those that were in its way stood off, and threw themselves down upon the ground; by which means, and by their thus guarding themselves, the stone fell down and did them no harm. But the Romans contrived how to prevent that by blacking the stone, who then could aim at them with success, when the stone was not discerned beforehand, as it had been till then; and so they destroyed many of them at one blow.
For "THE STONE COMETH", Williamson translates rather, "Baby on the way!" Turns out the original Greek (i.e. the translation Josephus had made of his original Aramaic) reads "ὁ υἱὸς ἔρχεται", meaning "the son cometh". The online commentary, which seems perhaps to have been written by Samuel Burder (1773–1836) has a rather impenetrable footnote caused by OCR of Greek characters (ΥΙΟΣ, ΥΙΟΣ and ΠΕΤΡΟΣ), as Latin (you can view a scan here) that suggests it does indeed say "son" in the original. I rather like Williamson's creative handling of it, then.
When the Romans came to besiege Jerusalem, they brought Josephus to try and negotiate a settlement. Josephus tries to argue the people are fighting not the Romans but the will of God, and gives a long list of how with God on their side, their ancestors had always prevailed, at one point saying (V.9):
In old times there was one Necao, king of Egypt, who was also called Pharaoh; he came with a prodigious army of soldiers, and seized queen Sarah, the mother of our nation. What did Abraham our progenitor then do? Did he defend himself from this injurious person by war, although he had three hundred and eighteen captains under him, and an immense army under each of them? Indeed he deemed them to be no number at all without God's assistance, and only spread out his hands towards this holy place, which you have now polluted, and reckoned upon him as upon his invincible supporter, instead of his own army. Was not our queen sent back, without any defilement, to her husband, the very next evening?—while the king of Egypt fled away, adoring this place which you have defiled by shedding thereon the blood of your own countrymen; and he also trembled at those visions which he saw in the night season, and bestowed both silver and gold on the Hebrews, as on a people beloved by God.
We know Josephus is (or at any rate, would be by the time he wrote Antiquities) knowledgeable in Jewish history; I can only assume here he's playing on the people's ignorance. Sarai was taken by Pharaoh (with no mention of any armies) when Abram had gone down into Egypt; this did not happen in Jerusalem at all, which had no significance as yet for Abram. Nor would it yet until after the war of the four kings and the five kings, when he met its king Melchi-Ṣedeq, and later on when God called on him to sacrifice his son on the mountain then above Jerusalem, and now at its heart. It's also not until the war of the four kings and the five kings that we learn he had three hundred and eighteen servants (not captains of armies!), and from the lack of mention of them anywhere else, the Midrash concludes that these three hundred and eighteen were but one person,Eliezer (the of whose name reaches that figure). The description of Sarah as "queen", however is not literal; it refers to her name, which means "princess".