Why specifically like "the dust of the earth"?
Targum Unk'lus and Targum Yonasan: There is nothing that is more numerous than the particles of dust. 1
Ha'Emek Davar: Even when you will be at your lowest in exile, you will flourish in all directions, and all the families of the earth will be blessed through you.
Seforno: It is when Yakov's children will hit rock-bottom that they will spring back and flourish in all directions. 2
Tosfos ha'Shalem (3): Yisrael are compared to the stars and the dust. When they ascend, it is up to the stars. When they descend, it is to the earth. 3
Tosfos ha'Shalem (2, citing R. Efrayim, from Bereishis Rabah 69:5): Earth outlasts metal vessels. Also Yisrael endure forever, and outlast all the nations.
See for example, how Yisrael proliferated in Egypt, from seventy to more than four million in the space of two hundred and ten years!
Hashem's salvation comes when things cannot get worse for Yisrael.
Oznayim la'Torah: This explains why Hashem associated 'the dust of the earth' with Yakov's children - whose sins cause brought about the Galus; but the 'spreading' to Yakov himself - since the Ge'ulah will come about via the Z'chus Avos.
What is the significance of the four directions?
Rashi: Not like Avraham, to whom Hashem promised only the whole of Eretz Yisrael (13:14,15) or like Yitzchak, to whom He promised all these lands (see 26:3).
See Oznayim la'Torah, who cites two opinions in the Midrash as to whether Hashem folded the whole of Eretz Yisrael underneath Yakov or whether it was just the Beis-Hamikdash - Either way, He only promised him that his descedents would would spread to the whole of the land that was underneath him (not to the entire world, like Rashi).
What did Hashem mean when he said "and all the families of the world will be blessed through you?
Targum Onkelus and Targum Yonasan: All the people in the land will be blessed due to you (and in your merit). 1
Rashbam: Refer to 12:3:2:4.
Seforno: Yisrael compared to the nations of the world are called Kohanim, 2 in which case they are the conduit which brings blessings upon the world.
Ohr ha'Chayim: Also Avraham received this Brachah. When he came to Aram, it was blessed. When Yakov came to Egypt, it was blessed. "Uv'Zar'acha"
Presumably, Rashi and Ramban explain similarly to above (Bereishis 12:3), i.e. people will say to their children 'be like Avraham!' (Rashi), and not only the people of Kena'an, but also the people all over the world will be blessed due to Avraham (Ramban).
Hashem promised to Avraham "north, south, east and west" (above, Bereishis 13:14). Why did He change the order here to "west, east, north south"?
Riva, Hadar Zekenim: Avraham went to the south, so Hashem promised to him first the north, from where he came. Yakov went to the east, so He promised to him first the west, from where he came.
Tosfos ha'Shalem (4, from Shmos Rabah 21:7): "U'Faratzta" is next to Yamah, to hint that in Yakov's merit, Hashem will make Pirtzos (breaches) in the sea (split it).
Tosfos ha'Shalem (8): There are 13 Brachos here corresponding to the Shevatim, which will all inherit [in the days of Mashi'ach] from east to west (Yechezkel Perek 48).
Malbim: Yehoshua will begin to conquer in the south from east to west, and afterwards to the north.
Why did the Torah use the word "v'Nivrechu"?
Refer to 12:3:2:4.
Why did Hashem tell Yakov "and all the families of the world will be blessed through you and your seed"? To Yitzchak, He told Yisrael (22:18) only that they will be blessed through his seed!
Ha'Emek Davar: The Brachah to Yitzchak was of tremendous wealth. Yitzchak himself had such wealth only with respect to the Plishtim, but not with respect to all nations