Is it permissible to appoint someone to perform the obligatory Hajj or 'Umrah on my behalf due to a travel ban for reasons of debt? And is it permissible to offer the sacrifice (Uḍḥiyah) with the intention of relieving distress and facilitating matters?

It is not permissible for someone to be deputized on behalf of a person who is physically able to perform the obligatory Hajj or Umrah. For example, a prisoner is not obligated to perform Hajj until after his release from prison, and deputizing someone on his behalf is not valid.

It is permissible to offer a sacrifice and distribute the meat to the needy with the intention of it being a sacrifice, alleviating distress, and facilitating affairs, for charity has a great effect in averting affliction. However, this is conditional upon it being free from corrupt beliefs, such as warding off the evil of jinn by shedding blood.