If a shraddha tithi falls on an Ekadasi day Will serving rice during the ceremony accrue sin? Can the kartha, kartha’s mother and brothers partake rice? Can a widow partake the offerings during shraddha of her mother or father?

If a sharaddham falls on an Ekadasi day, rice must be served to the Brahmins who are invited to act as manes because the home (sacrificial fire ritual) is performed with rice; huta sesham is associated with the ritual. Hence, only rice must be included in their serving
Since the shraddham is on Ekadasi, the kartha must not partake rice
Widows are allowed to partake the offerings during the shraddham of their mother or father; but they must not partake rice if the shraddham is on Ekadasi.
NOTES
If shraddham falls on Ekadasi, rice must certainly not be consumed. One must also not consume any preparation that has not been offered during the ceremony. It appears only bhakshanams and cooked vegetables alone can be consumed.