Is the young man's not meeting the director of a study center, with whom he had a disagreement regarding the price of a training course, considered forbidden abandonment (hajr muharram) that prevents deeds from being presented to Allah Almighty, and is he obligated to search for the aforementioned director?

Not meeting is not an unlawful abandonment (hajr). You are not considered to be abandoning someone as long as you do not turn away from them when you meet them and refuse to greet them. Nor is it obligatory to search for them. However, if you do meet them, you must greet them with salaam so that the abandonment is removed, according to most scholars.