Who exactly, accompanied whom, when they left Ur Kasdim on their way to Eretz Kena'an?
Rashi: Terach and Avraham left accompanied by Lot and Sarai. 1
Ramban: Upon leaving Ur Kasdim, Terach may well have taken his entire family with him. Lot and Sarai, however, accompanied (not Terach, but) Avraham, who was more important than his father. 2
What prompted Terach to set out for Eretz Kena'an at this time?
Seforno: Eretz Yisrael was special (it seems already then), as the Torah will later write about it "The land which HaSh-m... seeks." 1 Indeed, "The very air of Eretz Yisrael makes a person wise" (Bava Basra 158b). 2
Proof of this lies in the fact that (as the Navi (Yechezkel 22:24) testified,) Eretz Yisrael was unaffected by the water of the Flood.
Why does the Pasuk conclude that they remained in Charan, and that Terach died there (11:32)?
Seforno (to 11:32): This teaches us that Terach lacked the conviction to carry through what he began. 1
Not so Lot, who did accompany Avraham (for a time) when he eventually moved to Eretz Kena'an. For this, Lot merited to share the lands that were given to Avraham (Amon and Mo'av were granted the lands of Kenizi and Kadmoni - Rashi to 15:19), a privilege that Avraham's other relatives did not merit. (In the future these lands too will revert to Bnei Yisrael - Rashi ibid..)