Part 1
Partially agree, MJ. 

At issue is your rejection of the PARTICIPATION OF THE FAITHFUL at mass as "worshiping," insisting instead on the term "assisting."  

I absolutely agree with you, possibly contrary to your meaning, that we all  "offer sacrifice." 

Sacrifice is essentially the primordial human action of "gift giving" when the gift is given to God (or a god). 

More specifically, our Eurcharistic Liturgy duplicates that form of Jewish sacrifice called a "communion sacrifice" (NJB translation), in which (1) worshipers bring a food-animal gift to the altar (2) for the priest to offer to God by killing and burning the animal (giving it to God by removing it from our use), and (3) God in turn invites the worshiper to share the gift as a roast at a communal meal.

(This is structurally the same guest bringing a bottle of wine or box of after-dinner-mints as a dinner gift, and the host serving that wine with the meal or sharing the mints after the meal.)