Is a young man whose father disappeared a long time ago and whose fate is unknown considered an orphan? And what is his duty towards his father of unknown fate, regarding prayer (Du'a) and answering questions related to him?

You have exceeded the age of orphanhood, because an orphan is someone whose father has died and who has not yet reached maturity. Your father is considered alive for you until evidence of his death is established, or a period of time passes after which it is highly probable he would not survive. This period is not fixed, and some scholars have striven to estimate it. The ruling of the judge must be considered; the mere passage of time is not sufficient. Your statement, "He is traveling," is not a lie. You may pray to Allah to return him to you if he is alive, and you may supplicate for his forgiveness and mercy, whether he is alive or dead.