On the Hyksos-Amalekites connection I first want to say I feel it's not quite that simple. The Hyksos were many tribes of Asiatic peoples. They included the Amalekites and possibly other Edomite tribes, I think they had a Midianite element too (Hor II of the 13th Dynasty I think was the Midanite king Hur mentioned in The Bible). Archaeology clearly shows they had an Amorite element as well. Ishmaelite and Aramean tribes could have contributed also to help explain some of the confusion of the Arabian historians.
I agree with Ages in Chaos about Agag being Apep.
The early Hebrew written signs as they are preserved on the STELE OF MESHA show a striking resemblance BETWEEN THE LETTERS G (GIMEL) AND P (PEI). NO OTHER LETTERS are so much alike in shape as these: each is an oblique line connected to a shorter, more oblique line, and is similar to the written number 7, THE SIZE. OF THE ANGLE BETWEEN THE TWO OBLIQUE LINES CONSTITUTES THE ONLY DIFFERENCE.There wasn't more then one known Agag though, Balaam is giving a Prophecy of the days of Saul. Though it's certainly not impossible more then one Amalekite King had that name including one contemporary with Balaam. The claim of there being more then one Apepi is also spurious and exists because of how Josephus's copy of Manetho is likely confused, but it's still not impossible more then one Hyksos ruler used that name. In both cases it is the latter one at the end of this period who certainly existed.
Nevertheless, it seems that not the Hebrew reading but rather the EGYPTIAN MUST BE CORRECTED....Almost EVERY hieroglyphic consonant [Egyptian] stands for MORE THAN ONE SOUND, and only empirically are all the sounds symbolized by a consonant found.
Velikovsky and others are wrong in citing Genesis 14 as proving the Amalekites existed already before Esau/Edom. The reference to them there is an editorial note from Moses, telling his readers where on the Map of their day he's referring to. Like how we often say "near modern _____". The Arabs didn't have an Arabic translation of The Bible until well after the Koran, so they got Amalek's genealogy confused just as they did how the Amalekite pharaohs relate to the history of Joseph and Moses.
Since Velikovsky's time Archeologists are inclined now to consider the location of Avaris indisputable. And thus his Al-Arish theory useless.
It could be the Hyksos used more then one city as their Capital (like the later Persian Empire, or Assyrian Empire), each of which could have been known as "ḥw.t wr.t", which means "Great House". And Velikovsky's model certainly does not preclude that they'd have some regional capital in the Delta.
Velikovsky's theory on the location of Sharuhen is probably wrong. This would have been the city they operated from when they attacked Ziklag. Judges 19:6 places Sharuhen in the allotment of Simeon. But the Edom-Seir region is indeed where Simeonites would wind up much later as we see in 1 Chronicles 4.
On the subject of Psalm 78:49 and "Evil Angels". I do not believe there is a scribal error here, I believe God's Word is preserved. But the idea that it's a Hebraic Pun on "Shepard Kings" is possible.
So I think I've covered everything on this subject I might disagree with Velikovsky on. I now want to talk about Greek Mythology.
Based on dating information from Eusebius, 1484 or 1470 BC is the date of Danaus leaving Egypt to found Argos. Revised Chronology places that during the Hyksos period, since the latest possible date for the Exodus is 1492 B.C. (Ussher's date).
Danaus (ancestor of the Spartan and Macedonian Royal houses according to mythology via Perseus and Herakles) is frequently identified with the Tribe of Dan by various theories. While I definitely consider the name evidence of Semitic origin, the D-n element does exist in Semitic languages independent of The Tribe of Dan, in Biblical names like Dinah and Dannah and Dedan and Daniel. But most relevant here is Dinhabah, the city of the first King of Edom in Genesis 36. (And some sources say the Ugarit story of Aghat and Pighat gives a Donatiya as the wife of Danel.) Later on I do believe a Danite intermarriage with this line happens via Andromeda daughter of Cephus of Joppa/Jaffa and Perseus.
Josephus's account of the correspondences between the Spartan King and the High Priest Onais about the Spartans having descent from Abraham refereed to the Spartan seal as being an Eagle clutching a Serpent. Extra-Biblical sources like the Targums are appealed to for evidence to make the Eagle a symbol of Dan. But Biblical evidence links the Eagle with Edom in Obadiah 4 and Jeremiah 49:16&22.
The Serpent is indeed linked to Dan, maybe the Eagle clutching a Serpent in part represents an intermingling of Edom and Dan?
The Sabine Tribe of Ancient Italy claimed descent from a Spartan colony according to Plutarch. Perhaps this can add to the Edomite heritage of Rome. Rome's second King was a Sabine.
The father of Danaus was Belus. Belus could come from Bela son of Beor, an Ancient Edomite King mentioned in Genesis 36, or maybe Baalhanan. The Amalekites were an Edomite tribe. Genesis entered it's finale form in the days of Moses, so 36 could include Edomite Kings contemporary with The Exodus.
If one of the two Hadad/Hadars who was a King of Edom in Genesis 36 is also the ruler deified as the Semitic god Hadad, then his name would also be linked to Baal/Bel. The last King of Edom listed here is Hadar in Genesis 36 but Hadad in Chronicles. His city Pau/Pai is unidentified and has been speculated by some scholars to be an Egyptian city, and that his wife Mehetabel is Egyptian in origin. Maybe Pau/Pai is Al-Arish/Avaris.
Belus was a King of Egypt, but that Danaus's brother(Aegytpus)'s name became the Greek name for Egypt is largely due to confused Greek geography. Like I discussed elsewhere with Aethiopia(Ethiopia).
Apollodorus ( 2.1.4-5)
"Belus remained in Egypt, reigned over the country, and married Anchinoe, daughter of Nile, by whom he had twin sons, Aegyptus and Danaus, but according to Euripides, he had also Cepheus and Phineus. Danaus was settled by Belus in Libya, and Aegyptus in Arabia."
Marrying a daughter of the Nile is likely a reference to him marrying a Native Egyptian (possibly of Royal or Nobel blood) for political reasons. Whether or not the Hyksos historically ever did that I don't think we know for certain.
Because I support the Arabian view of Mount Sinai, I'm aware that what Arabia meant to Ancient Greek Writers (Modern Jordan south of the Dead Sea and north western Saudi Arabia) is where the Israelite wondering was, this included ancient Edom. Some scholars think classical Arabia could have included parts of southern Israel (south of Beersheba) and the north eastern Sinai Peninsula, which would include Al-Arish.
So it sounds like Belus may have put his Heir Apparent in charge of the Amalekites original homeland. Like how the Welsh in origin Tudors monarchs of England began making the Crown-Prince the Prince of Wales.
Greek myths go on to tell us that Aegytpus conquered a people called Melampodes. Malampodes means "black footed" and could make sense as a term for former slaves who made mud bricks with their feet. So I think they're the wandering Israelites and that this is a reference to not the first post Exodus Amalekite encounter, but when the Amalekites were victorious over them in Numbers 14:45.
In Peoples of The Sea on pages 84&85, Velikovsky argues for Temeh or Temehu being a name the Egyptians used for the Spartans or Lacedaemonians. Teman is in Genesis 36 the name of a grandson of Esau (brother of the grandson Jasher links to Rome, and Amalek was their half brother), and later in The Bible a region in Edom. The same basic Hebrew word is sometimes used and translated South, and the Teman in Edom is possibly one of it's more southern locations. So perhaps Edomites who colonized the Peloponnesian peninsula used a word similar to Teman for the southern most region of the Peloponnese, where Sparta/Lacedaemonia was?