#For what did Yahweh say that only Aaron, his sons, and his ancestor's clan would be responsible?

Yahweh told Aaron that he, his sons, and his ancestor's clan would be responsible for all sins committed against the sanctuary. [18:1]

#Who did God say would be responsible for all sins committed by anyone in the priesthood? 

Only Aaron and his sons would be responsible for all sins committed by anyone in the priesthood. [18:1]

What would happen if the Levites profaned the holy offerings of the people of Israel?

If the Levites profaned the holy offerings of the people of Israel, they would die.