Is it obligatory to inform the sister of the financial amounts that the mother gave to her daughter during her lifetime, and is the daughter entitled to take anything from the inheritance despite the existence of these amounts?

There is no need to inform the sister about the gift. The leftover money is to be divided among the legal heirs, including the questioner. What was taken from the gift during the mother's lifetime does not prevent one from taking their legal share. Even if the gift was unjust, it becomes definitively owned by the donee upon the death of the donor.