Is it obligatory to re-issue Zakat al-Fitr if it was previously given as money without verifying whether the recipient was Muslim? And is the Zakat valid if it was given as food and money with the intention that the food is the Zakat and the money is merely assistance? And what is incumbent upon one who has diligently (ijtahada) engaged in jurisprudential matters without knowledge, then imitated a scholar?

Scholarly opinions have differed regarding the permissibility of giving monetary value for Zakat al-Fitr. The majority of scholars hold that it is not permissible, while the Hanafis, Bukhari, and others consider it permissible. What your mother did by giving the monetary value is, God willing, sufficient. If Zakat was given to someone she thought was a poor Muslim, and then it turned out otherwise, she is not required to give it again, even though some scholars permit giving it to people of the Book (Ahl al-Dhimma). As for repeating the payment in food after having already paid money, there is no harm in it, and she will be rewarded for it. You should be gentle with your mother in offering advice.