Is the money my mother used to take from her father's pension after my father's death, and then after her second marriage, considered a debt upon her? Was it unlawful, and if so, how can I repay this debt or dispose of this money?

The pension your mother received after your father's death is a grant from the issuing authority, and the conditions for its entitlement are determined by that authority. You are not permitted to withdraw the pension except after consulting the issuing authority and informing them of the situation. If they grant you permission and you absolve your mother of what she spent, then there is no harm. If you are obliged to repay what your mother received while she was married, then it must be repaid from your mother's money, if available.