Praesta, quaesumus, omnipotens Deus,
ut nullis nos permittas perturbationibus concuti,
quos in apostolicae confessionis petra solidasti.
There is nothing especially difficult about the grammar and vocabulary of this prayer, though it is theologically profound. NB: the solidasti is really solidavisti, a "syncopated" form.
Ecclesiae tuae, quaesumus, Domine,
preces et hostias benignus admitte,
ut, beato Petro pastore,
ad aeternam perveniat hereditatem,
quo docente fidei tenet integritatem.
This is a good deal harder than the Collect. From the point of view of vocabulary, trying to get the right sense of admitto helps to establish the "mood" of the prayer. Admitto carries the weight of "suffering" or "allowing" something to enter into one’s presence. "Admit" is more eloquent than just "receive". Admitto immediately lends a sense of God’s highness and our needy lowliness, waiting upon God’s good pleasure. Grammatically, you have to get that quo docente right, or nothing else works. I think the trick here is to avoid taking quo docente as an ablative absolute (which is what beato Petro pastore clearly is) and instead see it as an ablative of "agent".
O Lord, we beseech Thee,
kindly suffer to receive the prayers and sacrificial offerings of Thy Church,
so that, blessed Peter being Her shepherd,
and, by whom as he is teaching holds fast to the integritry of the Faith,
She may attain to the eternal inheritance.
Deus, qui nos,
beati Petri apostoli festivitatem celebrantes,
Christi Corporis et Sanguinis communione vegetasti,
ut hoc redemptionis commercium
sit sacramentum nobis unitatis et pacis.
Commercium is a loaded word. It means "exchange". It has a theological, not a mercantile sense, of course. Bread and wine were chosen by God, from all gifts He gave us, to be transformed into His Body and Blood.
O God, who with the Communion of the Body and Blood of Christ,
has nourished us celebrating the feast of the blessed Apostle Peter,
grant, we beseech Thee,
that this sacred exchange of redemption
be for us a sacramental sign of unity and peace.
We chose from among those gifts of bread and wine, those concrete gifts which we offered at this particular Mass. They were a symbol of something from to be offered ourselves, to be returned to the one who gave them. God accepted them, and transformed them through His Spirit into the Body and Blood of Christ. Then gave them back to us, so that we, through them might be transformed more and more into what they are. This is an amazing interchange of gifts, God always having logical prioroty over the giving and the given. Thus, in the process, we are united to God and each other in a marvelous sacred "exchange".