These are the commandments and the ordinances, which Hashem commanded by the hand of Moshe to the children of Israel, in the plains of Moav by the Jordan at Jericho. (Bamidbar 36:13)
These are the words which Moshe spoke to all Israel beyond the Jordan; in the wilderness, in the Aravah, opposite Suf, between Paran and Tofel, and Lavan, and Hatzerot, and Di-zahav. Eleven days journey from Horev, to Kadesh-barnea, by the way of Mount Seir. (Devarim 1:1-2)
The last verse of Sefer Bamidbar specifies that the preceding commandments were commanded in Moav. The first verse of Devarim does not specify where the commandments which follow were given. In fact, in chapter 5 we will learn that they were given at Sinai.
I personally think (like Ibn Ezra) that at least some of the places listed here represent separate locations, each of which Moshe gave the "speech" of Sefer Devarim over again. Certainly Kadesh-Barnea seems logical in that respect, since the content of Sefer Devarim addresses the entry to Israel, and the Jews would have entered Israel from Kadesh-Barnea (after a journey from Horev[=Sinai] via Hatzerot) were it not for the spies incident.
Devarim is referred to as "Mishneh Torah". Perhaps that means "orally repeated Torah", as in "veshinantam lebanecha", as the speech was repeated orally several times. (R' Menachem Leibtag)
And it came to pass in the fortieth year, in the eleventh month, on the first day of the month, that Moshe spoke to the children of Israel, according to all that Hashem had given him in commandment unto them; after he had defeated Sichon the king of the Amorites, who dwelt in Heshbon, and Og the king of Bashan, who dwelt in Ashtaroth, at Edrei. Beyond the Jordan, in the land of Moav, Moshe took upon himself to expound [?] this law, saying: "Hashem our God spoke to us in Horev... (1:3-6)
There is no punctuation in the written Torah, so you have to mentally add it yourself. Here we clearly have an "open-quote" as Moshe begins his speech. Where is the close-quote? I think it comes four chapters later, after verse 4:40. Then there is another open-quote in 5:1. This begins a speech which continues all the way until 26:19. The final 8 chapters of Devarim, after this mega-speech, contain miscellaneous other topics. (R' Menachem Leibtag)
Verses 3-5 seem redundant after verses 1-2. See the explanation here.
Then Sichon came out against us, he and all his people, to battle at Yahatz. Hashem our God delivered him before us; and we smote him, and his sons, and all his people. (2:32-33)
Why the mention of Sichon's sons, which does not appear for the other battle (with Og)? Presumably this is because his sons were the generals leading the battle. We find the same phenomenon with Shaul, and it was likely the case with some other ancient kings. As one example with Shaul, his son Yehonatan led battles against the Philistines. (Shmuel Alef 13:3,14:1-14:14)
As another possible example, there is the disturbing story in Shmuel Bet 21, where it is revealed after Shaul's death that he had massacred the Giveonite people. As a form of reparation, the remaining Giveonites request that seven of Shaul's sons or descendants be put to death, and David does this. Not only does it seem immoral for there to be arbitrary punishment, but the Torah specifically prohibits punishing sons for the crimes of their fathers. But if these sons had been army commanders like Yehonatan (Yehonatan himself had previously died in battle), then it makes perfect sense that they be put to death for a crime which they themselves committed. This would, perhaps, have been the first war crimes tribunal in history.
(Verse 21:7 would still need explaining though.)