Is it permissible to perform Hajj on behalf of a deceased father 17 years after he made a vow, and is it permissible to appoint someone to perform Hajj on his behalf?

This vow falls under the category of a vow of obedience, which must be fulfilled, based on the Prophet's (peace be upon him) saying: "Whoever vows to obey Allah, let him obey Him." Therefore, you must perform Hajj on behalf of your father. If you are unable to do so, then appoint someone to do it for you. The vow is not nullified by the passage of years as long as you are physically or financially capable of fulfilling it.