Is it permissible to pay a portion of the shop's zakat in cash to the Zakat Authority based on the fixed capital in the commercial register, and then pay the remaining portion of the obligatory zakat in cash and provisions to charitable organizations?

There is no disagreement regarding the permissibility of giving zakat (definition) on trade goods in cash. As for giving its value in merchandise, the fatwa (definition) permits it when there is an overriding benefit, not absolutely. This is provided that it is not a ruse to give out inferior items, but rather that the zakat is given from goods of medium quality.