К предложениям нужно задать 5 вопросов(общий,альтернативный,специальный,к подлежащему,разделительный) 

1) My friend entered the Medical Institute last year.
2) All students take exams in winter.
3) The delegation will leave Tomsk on Monday.

Did my friend enter the medical institute last year? Does не подойдет вместо did?

Нет, это прошедшее время. Написано же Last Year - в прошлом году. А Does - время настоящее.

Спасибо Вам большое!

Did my friend enter the medical institute last year?Did my friend enter the medical or the economy institute?Where did my friend enter last year?Who did enter the medical institute last year?My friend entered the medical institute last year, didn't he? Do all students take exam in winter?Do all students take exam on winter or on spring?When do all students take exam?Who does take exam on winter?All students take exam on winter, don't they?Will the deligation leave Tomsk on Monday?Will the deligation leave Tomsk on Monday or on Thursday?When will the deligation leave?Who will leave from Tomsk on Monday?The deligation will leave Tomsk on Monday, won't it?