What width did he measure?
Rashi: The interior of Ezras Nashim.
Malbim: The width of Ezras Nashim. As long as he was in front of the chambers, he could not measure, for the chambers were in the inner side of Chatzer ha'Penimi with the cells, and both of them extended until 40 Amos from the gate. All this is called Lifnei ha'Sha'ar. After the chambers and cells finished after 40 Amos, he measured from the inner wall of Chatzer ha'Chitzonah to the outer wall of Chatzer ha'Penimi.
What is "[mi'Lifnei] ha'Sha'ar ha'Tachtonah"?
Rashi: It is the gate discussed above. Radak - "Tachtonah" is like Tachton. The Hei is extra, for Sha'ar is masculine; therefore, it is mi'L'eil - the accent is on the penultimate syllable, the [latter] Tav. The gate of Ezras Nashim is called "Tachtonah" compared to the gate of Chatzer ha'Penimi, (Ezras Yisrael), for Ezras Yisrael was higher than Ezras Nashim. The mountain [on which the Mikdash was built] sloped; the west was higher than the east. One ascended [to Ezras Yisrael] via seven steps.
Vilna Gaon: From the Eil at the end of Sha'ar ha'Chitzonah to the Eil at the beginning of Sha'ar ha'Penimi.
Malbim: It was after the 40 Amos, after which ended the chambers in front of Sha'ar ha'Tachtonah.
Up to where is "Lifnei he'Chatzer ha'Penimi [mi'Chutz]"?
Rashi: It is until Ezras Yisrael.
Radak: This measure is without Sha'ar ha'Penimi. Vilna Gaon ? this is because Sha'ar ha'Penimi stuck out from Chatzer ha'Penimi.
Malbim: It is where ended the cells in Chatzer ha'Penimi outside. There the wall was open on both sides
What is the meaning of "ha'Kadim veha'Tzafon"?
Rashi, Radak: In the two directions, [from west] to east and north [to south], its interior was 100 Amos.
Malbim: After he measured in the east, he measured also in the north from wall to wall, and found that it was [also 100].