Is it permissible for the husband to give his wife a general permission to go out for necessities without informing him each time?

It is permissible for a wife to leave her husband's house out of necessity without his permission, but it is not permissible for any other reason except with his permission.

Disobedience (nushuz) occurs when she leaves her husband's house without his permission, unless she leaves to go to a judge to seek her rights, or to earn her maintenance if her husband is unable to provide it, or to seek a religious ruling (fatwa) if her husband is not knowledgeable in religious matters and has not sought a ruling for her.

If the husband permits his wife to leave, there is no harm, unless her leaving involves a violation of Islamic law or temptation (fitna), in which case he is not permitted to give her permission.