English Translation
Yamada isn’t popular with girls in his own grade, but he’s popular with the younger girls at school.
下級生 vs. 後輩 / 後期: when do you use which? Is one more formal than the other? Which one is more common?
後期 means “later term/stage”. It doesn’t refer to a person but a certain time period only. So, 後期 is not interchangeable with 後輩 or 下級生.
下級生 is more likely to be used among the current students, and just illustrates the difference of grades (school years) while 後輩 can be used also by alumni, or describe the close relationship between two+ people.
山田君は下級生にモテる. = Yamada-kun is a current student, and he is popular with younger girls at the same school.
山田君は後輩にモテる. = 1) Yamada-kun has already graduated from a school, and he is popular with the current female students at the school.; 2) Yamada-kun is a current student and joins a basketball club, and he is popular with younger female club joiners. (i.e. 後輩 means a more intimate inner circle than just going to the same school); or 3) Yamada-kun works for a company, and he is popular with younger female workers there.
If you say 山田君は高橋君の後輩です, it implies that Takahashi-kun is superior to Yamada-kun in terms of capability or organizational ranking; or that Takahashi-kun is ethically responsible for taking care of Yamada-kun’s personal development. If you swap the subject and the object, 高橋君は山田君の先輩です. The connotation of 先輩 is “Yamada-kun looks up Takahashi-kun”.
下級生/上級生 don’t have such a connotation. They just tell you the gap in school admission years.