1. I think that is a complete sentence. It is what I would call a directive. Please go to the store for me.
Be a roll model for your classmates.
2. His emotional outburst tended to cause an unwholesome impact.
3. Because of his fascination with the girl, he did not hear the teacher.
4. Her little sister was chosen for the games. (past)
She is playing today. (present)
She will be playing next week. (future)