Is it permissible for my mother to perform the Farewell Tawaf (Tawaf al-Ifadah), which she left unperformed during Hajj, while she is observing the 'iddah (waiting period) after her husband's death?

The Farewell Tawaf (Circumambulation) is one of the pillars of Hajj; Hajj is not valid without it. Whoever misses it remains in their state of ihram until they perform it. Therefore, your mother is still in a state of ihram and must return to Mecca to perform the Farewell Tawaf and the Hajj Sa'i if she has not already performed it. If she is in her iddah (waiting period) due to the death of her husband, she must observe the iddah in her home until it ends, then she can go to perform the Tawaf. This is because the time for the Farewell Tawaf is extensive, whereas the time for observing iddah at home is specific and will be missed.