Is it permissible to seek forgiveness for Muslim men and women with the intention of benefiting them, and to seek forgiveness for one's parents with the intention of honoring them when one is unable to control anger or visit them due to social phobia, and because the mother does not visit her relatives?

Seeking forgiveness for Muslim men and women is recommended, and it benefits them. The Prophet, peace and blessings be upon him, commanded it, and it is a charity. Seeking forgiveness for one's parents is an act of righteousness towards them. Seeking forgiveness for relatives is considered good, righteous, and a way of maintaining kinship ties. If you are unable to visit your relatives, you should try to overcome this and seek Allah's help. If you strongly believe that harm will befall you, then there is no blame upon you for abandoning that which would cause you harm. Parents have a right to connection, righteousness, and good companionship that no one else has.