Is the mother obligated to share equally with the partner of the deceased father in the commercial establishment's business? And should the borrowed amount be returned at its value at the time of borrowing or at the time of repayment? And what should be done with the money if its owner refuses to take possession of it?

Your father's friend is a claimant. If he has evidence of the partnership, then that is sufficient. Otherwise, your mother must take an oath to deny the claim. The man is only entitled to the amount stated in the document (two thousand dinars) as a debt owed by your father, and the change in the dinar's value is not to be considered. If the issue cannot be resolved, it is recommended to refer it to the Sharia courts.