Is it permissible for the mosque to determine the value of Zakat al-Fitr in cash, then convert it into various food commodities other than those whose value was specified (such as rice, dates, and raisins), and distribute them to the poor? And does buying oil and ghee fall under the categories of Zakat expenditures?

What you are doing is a blessed charitable act, and you are agents for others. There is no requirement to differentiate between the funds of the donors. Rather, it is sufficient to purchase Zakat al-Fitr from the staple food of the country and distribute it to those who are eligible. However, purchasing oil and ghee is not permissible. It is important to note that purchasing dates with the value of rice may not fulfill the required number of sa's, unless you purchase more than what is necessary.