Is it permissible to perform an 'Umrah on behalf of the father from Al-Taneem after completing an 'Umrah for the mother or after performing Hajj on her behalf, and is the Farewell Tawaf obligatory before the additional 'Umrah in this case?

It is a great act of righteousness to perform Hajj or Umrah on behalf of your parents. After completing the Umrah of Tamattu for your mother and before entering into the state of ihram for Hajj, it is permissible for you to perform Umrah for yourself or for someone else. The same applies after completing the rituals of Hajj. According to the Shafii school, the farewell circumambulation (Tawaf al-Wada) is obligatory for everyone departing from the Sacred Precincts if their departure is for a distance that permits shortening prayers, or if their departure is for a shorter distance without the intention of returning. However, the majority of scholars view the farewell circumambulation for Umrah as a sunnah (recommended) and not obligatory.