Who was the King of Edom that the Jews exchanged messages with?
"And Moses sent messengers from Kadesh to the king of Edom" (Numbers 20:14)
His name was not mentioned on purpose according to the Ramban (Numbers 20:14):
The Torah did not write his name for there is no purpose for that, but then it does mention Sichon and Og, kings of the Emorites, with their names because they were known for their might and had a name among the nations, and this was done to thank the Blessed One for what He did for us
And the Torah writes 'And Edom answered', for all the officials agreed with him [i.e. the king of Edom] in this refusal
The Meshech Chochma writes in a similar fashion (Numbers 20:17):
See also Sefer haYashar (Chukas), Rashbam (Genesis 36:1) and Ibn Ezra (Genesis 36:31)
It is not written here "king of Edom" unlike regarding Sichon, because they had a legislature / parliament. And it also says (Obadiah 1:2) "small I made you among the nations and very despised" - for they don't have a king son of a king (i.e. a hereditary monarchy) [based on the Talmud Avodah Zarah 10a). Therefore, in a place that kingship is not inherited, the main thing is the agreement of the people, which is why it says "and Edom answered", "and Edom refused".
There is another opinion that his name was Haddad (see Genesis 36:35), as the Vilna Gaon writes in his commentary on Chronicles (I Chronicles 1:43):
"before there was a king in Israel" - this is Moses as it is written "and there was in Jeshurun a king". Therefore, the Torah does not mention the death of Hadad because he was still alive in the days of Moses (and died 5 years later as it is written in Sefer haYashar), only that his kingdom began before Moses. But in the days of Ezra he was already dead, and therefore it is written here "and Haddad died"
Who was the Canaanite, king of Arad?
"And the Canaanite, king of Arad, who lived in the south, heard that the Jews came through Atharim, and he fought them, and captured some captive" (Numbers 21:1)
This was Amalek, as it says "Amalek lived in the land of the south" (Numbers 13:29)Rashi's source appears to be a Midrash (Bereishit Rabba 19:20 and Tanchuma 4:6)
However, the Talmud (Rosh Hashanah 3a) tells us that this was Sichon (also see Tosfot there):
Sichon, Arad and Canaan are the same. Sichon because he was similar to a young donkey of the desert, Canaan because of his kingdom, and this real name was Arad. According to others, he was called Arad because he was similar to a wild donkey of the wilderness, Canaan after this kingdom, and his real name was Sichon.
Ibn Ezra (Numbers 21:1) and Ramban (Numbers 21:1) cite an opinion connecting this verse to a place called "Arad", later on (Judges 1:16):
And the children of Kenite, Moses's father-in-law, went up from the city of palms together with the Children of Judah into the desert of Judah, which is in the south of Arad, and they went and lived there.(See both Ibn Ezra and Ramban for further discussion)
What happened to the Miriam's Well after the Land was conquered?
"And the Jews arrived, the entire congregation, in the Zin desert, in the first of the month, and the people lived there in Kadesh. And Miriam died there, and was buried there" (Numbers 20:1)
When Miriam died, the well stopped as it is written: "and Miriam died there and was buried there" and right after it is written: "and there was no water for the congregation". And it returned in the merit of both of them (i. e. Moses and Aaron).
Once Miriam died, the well stopped and it came back in the merit of both Moses and Aaron. Once Aaron died, the cloud stopped, and both [the well and the cloud] came back in the merit of Moses. Once Moses died, all three stopped and did not come back.
Rav Chiya says: One who wants to see the Well of Miriam should ascend to the top of Carmel, and gaze and see something like a sieve and that is the Well of Miriam
Carmel - a mountain on the shore of the seaWe are not told what sea this mountain is near.
The Midrash tells us that the Well of Miriam is in the sea of Galilee (also called the sea of Tiberias), as written in Bamidbar Rabbah (19:26) and Midrash Tanchuma (1:39 and 4:6) - also cited by Rashi (Numbers 21:20):
"and it looks on the face of the wilderness" (Numbers 21:20) - this is the Well that came with them until it entered the sea of Tiberias. One who stands in the wilderness can look inside the sea and see something like an oven and this is the well that "looks on the face of the wilderness".
There is also a story cited in several Midrashim about an ill man getting healed from the Well of Miriam (Bamidbar Rabbah 18:22, Midrash Tanchuma 4:6 and 1:39):
There was once a blind man with boils who went down to immerse himself in water [some add "in a cave"] and the Well of Miriam appeared to him. He immersed himself and was healed.
There was once a man with a skin disease, who went down to immerse himself in the sea of Tiberias. The Well of Miriam appeared to him and he was healed. Where can it found? Rabbi Chiya bar Abba said: it is written "and it looks on the face of the Yeshimon (literally wilderness)" (Numbers 21:20). For anyone who goes up to the mountain Yeshimon, he will see something like a small sieve in the Sea of Tiberias, and that is the Well of Miriam.This is also cited in the Jerusalem Talmud (Kelayim 9:4 and Kesuvos 12:3)
In Sefer Shaar haGilgulim, the location of the well is narrowed down further:
When one goes on the shore of the Sea of Tiberias towards the hot springs of Tiberias, in the middle of the road literally, in a place where there are many pillars on the sea shore, and it is opposite a tower on the head of the mountain, that is where the Well of Miriam is.
[Published at parshapeople.blogspot.com]