Here "up to the heights" refers to a temple or altar that was built on high ground like a hill or mountain side. Alternate translation: "went up to the temple on the hilltop to weep" (See: [[rc://en/ta/man/translate/figs-idiom]])
These place names refer to the people who live there. Alternate translation: "the people of Moab will weep because of what happened to the cities of Nebo and Medeba" (See: [[rc://en/ta/man/translate/figs-metonymy]])
They do this to show their extreme sadness. Alternate translation: "They will all shave their heads and cut off their beards and grieve" (See: [[rc://en/ta/man/translate/translate-symaction]])