入学 and 卒業: entering school and graduating
Distinguish entering school from completing its course and graduating.
Entering as a student
入学 (にゅうがく) means entering a school as a student. 「四月に大学に入学しました」 says that the speaker entered university in April.
Merely entering a school building is not normally 入学. 「校舎に入りました」 describes physical entry into the building.
Completing the course
卒業 (そつぎょう) means graduating after completing a school's course. 「去年、高校を卒業しました」 says that the speaker graduated from high school last year.
「卒業する予定です」 expresses a plan or expectation to graduate. It does not mean a diploma has already been received.
Particles and educational stages
Learn the typical combinations 「大学に入学する」 for entering university and 「大学を卒業する」 for graduating from it. Do not treat both as the same direction of movement.
「卒業してから別の学校に入学しました」 describes graduating and then entering another school, both completed. It is not a purpose statement about needing to graduate in order to enroll.
Does 「入学試験に合格しました」 mean every enrollment procedure is complete?
Show the answer and why
No. It means passing the entrance exam. Actual enrollment and completion of further procedures are separate.