Is a house that the grandfather did not own with a title deed, and which was transferred to his wife after his death, considered an inheritance that must be divided among all heirs?

If the state gave the house to your grandfather's wife, whether for a fee or for free, then it belongs to her, and it does not become an inheritance for your grandfather. This is because inheritance is a branch of ownership during life, and your grandfather was not the owner of the house, but rather had the right of usufruct.