1) your mother can file complaint under Dv act seek maintenance from her husband . also seek right to stay in matrimonial home . this is based on presumption that no valid divorce has taken place
2) for valid divorce it is necessary that divorce decree should have been passed by court .
3) customary divorce has no legal sanctity .
4) it is necessary to go through documents relied upon by your father regarding proof of divorce .
5) if it is self acquired property of your father then you have no share in father properties . only if your father dies without a will would you get share in said property
6) your mother can inspite of divorce seek maintenance from her ex husband