Is it permissible for the wife to take a sum from her husband's salary—who does not pray and spends half his salary on smoking—in order to give it in charity, especially after he took all her gold as a debt and refused to repay it, claiming that he fed her with its price?

If the husband takes his wife's gold with the intention of returning it, it becomes a debt upon him, and he must repay it. It is permissible for the wife to take her due from his money without his knowledge if he refuses to repay.

As for the husband abandoning the obligatory prayers, it is a great sin. He must be commanded to pray, and the danger of abandoning prayer must be explained to him. If he does not repent and maintain his prayers, there is no good for the wife in remaining with him, and she should separate from him.