Why does it say "ha'Sefer ha'Miknah"?
Radak: Sometimes there is a Hei even though it is Samuch, e.g. "ha'Mamlechos 1 ha'Aretz" (25:26), like I explained above (refer to 25:26:1:1).
Texts that say 'Mamlechos ha'Aretz' are mistaken. (PF)
Did he give to him only "Sefer ha'Miknah"? Verse 14 says that there were three documents!
Radak: He gave to him also the other documents (refer to 31:11:2:3). The verse mentions only Sefer ha'Miknah, which was primary.
Malbim: He gave to him also Sefer ha'Galuy.
Why did he give the documents to Baruch?
Malbim: Baruch lived a long time after Yirmeyah, and returned from exile. He will give them to Yirmeyah's heirs.
Why is he called "Chanam'el Dodi"? He was Ben Dodi (verses 8-9)!
Rashi: Yirmeyah had a cousin Chanam'el, and also an uncle Chanam'el. If not, I do not know why the verse changed.
Rashi: Some say that he was Yirmeyah's uncle and his cousin. E.g. if Reuven married the daughter of his brother Shimon, and she gave birth to Nemu'el, and Shimon has a son Yemin, Yemin is the uncle of Nemu'el (his mother's brother 1 ) and also Ben Dodo (the son of his father's brother).
Radak: "Dodi" means Ben Dodi. Also "Lot Achiv" (Bereishis 14:16) means Ben Achiv.
Rashi: This is wrong. We do not find anywhere in Tanach that the mother's brother is called Dodo!
What is the meaning of "ha'Kosvim b'Sefer ha'Miknah"?
Radak: They signed their names in it for testimony.