Both 그 시절을 살다 and 그 시절에 살다 are correct and often interchangeable, but there is a small nuance difference. 그 시절에 is used more to introduce concrete details of what happened during that time, whereas 그 시절을 treats the period as an indivisible unit that one lives, passes by, remembers, forgets, or otherwise treats as a single entity. For example: 1. 그 시절에(는) 공부도 하고 친구도 사귀며 즐겁게 살았어 = I lived that happy time studying and making friends. 2. 그 시절을 참 어렵게 살았어 = I lived that time in hardship. (그 시절에(는) is also possible) In #1 그 시절에 as an adverbial phrase sets the stage for more details. In #2 그 시절을 is an object of the verb - it plays a major part at a high level. In 그 시절을 아직 살아가는 한 사람, it is saying that he is still living like he's in that period rather than forgetting it and moving on. Since the point is about remembering and reliving the period and not day-to-day details, 그 시절을 is more appropriate.

에 is used to indicate location usually like 학교에 - at school. Since 시절 isn't a location, you use 을.

what is that????????