ayah1
Answered

The teacher asked that each student completes/complete the exercise.

Acomplete
Bcompletes

The student wished that his mother was/were more lenient about his curfew.

Awas
Bwere

If he was/were a good runner, he would be a great addition to the track team.

Awas
Bwere

The principal required that each teacher submits/submit their grades online.

Asubmits
Bsubmit

The captain wishes that his team was/were more motivated to win state.

Awere
Bwas