Is the questioner required to inform the administration that he was the one who complained about the teacher to the board of directors? Is there an expiation for his lie? And what is the recompense for someone who guides people to truthfulness but does not practice it himself?

Lying is forbidden. If disclosing that you are the complainant would lead to harm, you are not obligated to inform the administration of that. Your repentance is achieved by abandoning lying, regretting it, and resolving not to return to it. As for your enjoining truthfulness while falling into lying, abandoning enjoining good and forbidding evil because of a sin is not required. Rather, what is obligatory is to reform oneself and persevere in enjoining good and forbidding evil with sincerity. The rebuke in the verse is for abandoning good deeds, not for enjoining them. A Muslim must align their words with their actions, and sorrow and regret are signs of sincerity. Allah accepts repentance and loves those who repent, and one who repents from a sin is like one who has no sin.