Is it permissible for the husband to take from his wife's money for Zakat al-Fitr or annual Zakat and disburse it as if it were a debt upon him, and is the Zakat counted for the wife in this case?

A woman's zakat on wealth is obligatory upon her, not upon her husband. She is permitted to give it to her needy husband if he is among those eligible to receive zakat, and it would not be a loan but rather a right for those entitled to it.

As for Zakat al-Fitr, it is obligatory upon the wife, and the husband bears the responsibility for it. If the wife pays it herself, she may give it to her eligible husband, and it will be sufficient.

If the wife volunteers to pay Zakat al-Fitr on your behalf, it will be sufficient, provided that you grant her permission. If you borrow from her and then pay it, it will be sufficient, and you will be considered the one who paid it, and you must repay the borrowed amount unless she forgives it.