Is it permissible for the wife to exchange the food allocated to her for money without her husband's knowledge, and is his knowledge a condition for that? What is the ruling on a husband who promises his wife to buy things but does not fulfill his promise despite being able to do so?

It is not permissible for a woman to take from her husband's money without his permission as long as he provides for her adequately. However, if he gives her her maintenance (nafaqa) or gifts her money, she may dispose of it without his knowledge, as long as it does not harm the husband's rights. The value of the maintenance a wife receives becomes her property, and she has the right to dispose of it as she wishes in permissible ways.

As for a man promising his wife to buy something that is not obligatory for him, fulfilling it is commendable. It may also fall under the category of permissible untruths between spouses, intended to please and foster affection, as mentioned in the hadith of Umm Kulthum bint 'Uqba. This is not intended to deceive regarding rights.