What did Yaakov have in mind when he compared Naftali to an Ayalah (gazelle)?
Rashi #1: He had in mind the valley of Ginosar, 1 whose fruit ripens quickly, before that of any other area of Eretz Yisrael. 2
Rashbam: Bnei Naftali were swift in battle like gazelles. 3
Targum Onkelos: He was referring to the good land, which fell in his lot.
Targum Yonasan: He is praising Naftali's agility, calling him a swift Shali'ach, with reference to the occasion when he ran swiftly to give his father the good news that Yosef was still alive, and when he ran from Kena'an back to Egypt, to fetch the document that proved Yaakov's rights to the Me'aras ha'Machpelah. 4
Da'as Zekenim #1: He praises Hashem for his portion, like a gazelle thanks its Maker for saving it from a trap. 5
Da'as Zekenim #2, Hadar Zekenim #2: When a gazelle is slaughtered and flayed, the skin cannot contain the meat. So Naftali's land cannot hold its Peros, for it has so many. 6
Riva: The feminine alludes to Devorah, who was from Naftali, and ruled over Yisrael.
Rashi #2: Naftali went with zealousness to fight against Sisera (Shoftim 4:6).
Malbim: Naftali's portion spread on the entire eastern border by the Yarden, and also from east to west, so it bordered all the Shevatim. Ayalah is a tree (Alah), like "Tachas ha'Alah" (Yehoshua 24:26), sometimes it is called Elah. 7 "Sheluchah" indicates that the branches spread out wide, like "Sheluchoseha Niteshu" (Yeshayah 16:8). Avshalom's hair was caught in a branch of an Alah (Shmuel II 18:9).
Ha'amek Davar #1: Naftali had gazelles, via which it would send letters. It says "ha'Nosen" (masculine), for it refers also to Naftali, whose mouth was able to give beautiful words. 8
Ha'amek Davar #2: Naftali would send their children to learn Torah from their neighbors, the family of Machir (i.e. the half of Menasheh in Ever ha'Yarden). Refer to 49:21:2:5.
Ginosar is [the valley surrounding] the Kineres Sea (Targum to Bamidbar 34:11). (CS)
Rashi: Like the gazelle, which runs more swiftly than any other creature.
When Esav claimed the rights as they were about to bury Yaakov. Also Moshav Zekenim brings this.
It seems that this is Hadar Zekenim's intent, but the wording is a bit awkward. (PF)
Eretz Yisrael is similarly compared to a deer. (If so, why was this said specifically about Naftali? - PF)
E.g. Bereishis 35:4. (PF)
Ha'amek Davar: Had it referred only to Naftali, it would have said 'v'Hu Yiten' in the masculine.
What are the "Imrei Shefer" (beautiful sayings) that he delivers?
Rashi #1 (citing Targum Onkelos): This refers to their fruits (refer to 49:21:1:1), which elicit thanks and blessings to Hashem.
Targum Yonasan: Nobody can surpass his beauty of expression when he sings songs of praise to Hashem. 1
Da'as Zekenim: They are nice branches.
Malbim: "Imrei" are choice branches at the top of the tree, as in "b'Rosh Amir" (Yeshayah 17:6).
Ha'amek Davar: "Imrei Shefer" are words of Torah. 2 (Naftali's descendants) Devorah and Barak emphasize in their Shirah (Shoftim 5:14) that their defeat of Sisera came in the merit of Torah study. Naftali drew his Torah teachings from their neighbors, the Mechokekim 3 of the family of Machir (i.e. the half of Menasheh in Ever ha'Yarden). Naftali (with Zevulun) would send students there to learn, and upon their return they would eloquently spread the Torah of their teachers.
With reference to Shiras Devorah, who was from Naftali (See also Ba'al ha'Turim).
Ha'amek Davar (to Devarim 33:23): Naftali would have both novel Torah ideas (Chidushim), and the eloquence to teach them to others.
Ha'amek Davar (ibid.): The families of Machir and Ya'ir, sons of Menasheh, had married into Yehudah. They were the Roshei Yeshivah (as per Yaakov's Berachah to Yehudah to be the Mechokek (49:10; refer to 49:10:1:1***)).