The readers from the first and second readings: do they have to read the universal prayers too?
No, they do not have to. The General Instruction of the Roman Missal, paragraph 71, states: “The intentions are announced from the ambo or from another suitable place, by the deacon or by a cantor, a lector, or one of the lay faithful.” It is for the priest-celebrant who presides at Mass to introduce and conclude the prayers, but the intentions themselves are not his function, but that of the deacon or one of the other persons mentioned in the quotation.
