In general, no, the time does not change as you cross the equator.
No.
Moving across the equator, or moving north and south in general, does not alter the time or the date. It is by moving east and west that you can alter the time and date. The most abrupt change comes at the International Date Line.
solstice
solstice
Areas farther north or south of the equator reception of the sun depends with the position of the sun at the time.
It depends how far north, or south, of the equator you live.
Depends on how far north or south you are from the equator.
Summer occurs south of the equator at the same time winter occurs north of the equator and vice versa.
Nov-Dec-Jan-Feb. Since most of South America is south of the equator, seasons are reversed from North of the equator. At the equator, it is warm all year.
Summer and winter
The Tropic of Capricorn is located South of the equator, although it is not in a fixed location; it varies over time.
Time zones change from east to west, so the correct answer is no. However they are not perfectly straight, so it is possible to be in a different time zone than a place north or south of you.