... about the OF Offertory Prayers.
The Ordo Missae of the Third Edition of the Roman Missal (23 ff) says that the two "Blessed are you ..." formulae are to be said "submissa voce" - with lowered voice (the earlier edition had said "secreto"). It adds that if there is no singing at the Offertory, the priest may (not must) utter them with a raised voice. If he does that, the Congregation may (not should) reply "Blessed be God ... ". In other words, there is NEVER an obligation to say these words loudly and there is never an obligation for the people to make a response..
The other formulae are to be said "secreto"; in other words they may never be said to be heard by the congregation whether or not there is singing. The fact that some clergy say them aloud is either out of ignorance or a well-meaning feeling that the people should not be deprived of these important words. In fact, they are not important words but merely designed to keep the celebrant recollected.
Deep down, the problem is that for very many Western clergy the idea that the Liturgy is an objective sacrificial action has been totally lost and replaced by the idea - fostered by Mass versus populum - that it is a performance for the edification of the people.
In the General Instruction of the Third Edition of the Roman Missal (141 ff) the "Blessed are you" formulae are ordered to be said "secreto"; which is not precisely the same as the "submissa voce" of the Ordo Missae. This is all the more striking in that the corresponding paragraph of the previous edition of the GI says neither. And the Third Edition of the GI adds that they are not to be said aloud if there is organ playing. There are here slight and curious inconsistencies.
However this may be, it is true that in each edition and in both the Ordo Missae and the General Instruction, the priest is NEVER obliged to say these prayers loudly and is NOT ALLOWED to do so when there is any sort of music. He certainly is not allowed - as some clergy do - to wait until the music is over so that he can then deliver them audibly!
The prayers at the Commixture and before the Priest's Communion are also ordered to be said "secreto".
Bishop Peter Elliot's Ceremonies of the Modern Roman Rite comments: "When there is no singing, the celebrant may still choose to say these prayers quietly. The 'silent' option is mentioned first in the missal".