What is "ba'Es ha'Hi"?
Malbim: It is during the seven years of conquest.
Below (15:14), it says that Kalev dispossessed the giants from Chevron!
Radak #1, Malbim: Kalev did so upon Yehoshua's command.
Radak #2: In Shoftim, Bnei Yehudah dispossessed them after Yehoshua died.
Radak #3: Really, in Yehoshua's lifetime Yisrael dispossessed Chevron and the giants. It is attributed to Kalev and Yehudah because Yehoshua gave to him Chevron according to Hashem's word, and they strove more to fulfill the Mitzvah. It says "va'Yelech Yehudah El ha'Kena'ani ha'Yoshev b'Chevron" (Shoftim 1:10), even though they already did so; it lists it together with what they conquered after Yehoshua died. 1
Malbim (10:37): Yehoshua conquered the city Chevron, and Kalev conquered the open areas around it and its Chatzeros.
Radak: The same applies to "va'Yilachamu Vnei Yehudah bi'Yrushalayim" (Shoftim 1:8). They fought previously; Melech Yerushalayim is one of the 31 kings that Yehoshua and Yisrael killed.
What is Har Yehudah?
Radak: It is called so based on its end. Before they took it, it was not called so.
What is Har Yisrael?
Radak: Refer to 11:16:2:1.
