Is the pension received by the father from social insurance - knowing that it used to take a portion of his salary when he worked in a usurious bank - permissible or impermissible, especially since there is no other source of income for the family?

It is forbidden to work in usurious banks, whether by directly engaging in usury or by assisting it. However, if someone worked there while ignorant of the prohibition, their salary is lawful for them, as Allah Almighty says: "So whoever receives an admonition from his Lord and stops, then he may keep what is past, and his affair is to Allah." (Surat Al-Baqarah: 275) Whatever money was taken before knowing about the prohibition is lawful for them. They must repent and leave the work. There is no harm for your father in taking the pension from social insurance and the end-of-service bonus for the period during which he was unaware of the prohibition.