Question

Hello Rabbi,
I am currently learning in a certain book the laws of counting the Omer, and I saw there a ruling that led me to an interesting discussion. 
1. The author there writes, based on the words of Rabbi Zalman, that according to the view that commandments do not require intention, if a person wanted to recite a blessing, for example, over a certain fruit, and suddenly his friend came and recited a blessing next to him over another fruit that he was holding, then the first person has fulfilled his obligation through the second person’s blessing. Since commandments do not require intention, it is enough that he heard his friend’s blessing even if he did not intend to fulfill his obligation through it. From this he also inferred regarding counting the Omer, that according to the common custom today, where the cantor recites the blessing and counts, by hearing his blessing there is a concern that the congregation has already fulfilled the obligation of the commandment even though they did not intend to fulfill it. Therefore his conclusion is that one should explicitly intend not to fulfill one’s obligation through the cantor’s blessing and counting, in order to avoid any doubt. For we see from the Shulchan Arukh in section 489, in the laws of counting the Omer, that it was concerned for the view that commandments do not require intention with regard to a blessing in vain. Therefore, one who answers his friend should not say to him, “Today is such-and-such of the Omer.” (Practically speaking, he writes there that even if one did not explicitly intend not to fulfill the obligation through the cantor, one may still recite the blessing according to the common custom today, because subconsciously he already has an opposite intention like that.)
And this is difficult for me: how can one say that he fulfilled his obligation? He has no connection at all to his friend’s words. Granted, if he recited the blessing himself and did not intend anything in particular, still his own speech is attributed to him and he fulfilled his obligation. But when his friend recites the blessing and he does not intend anything at all, two things are lacking here: both any connection to the speech that came from his friend’s mouth, and also the lack of intention to fulfill the commandment. And the first lack seems more fundamental; presumably even the view that commandments do not require intention would agree that this is needed.
2. I saw that the Mishnah Berurah in section 60, subsection 7, wrote that there are two types of intention: one is intention regarding the words of the commandment itself—that he should not divert his attention to something else, and should listen to what he is saying with his mouth—and on this everyone agrees that intention is required (even according to the view that commandments do not require intention), though after the fact, if he did not intend, he has still fulfilled his obligation. The second intention is to fulfill the obligation of the Creator’s commandment, who commanded us to do this commandment; and regarding this intention there is a dispute whether commandments require intention or not. According to the view that they do require intention, even after the fact he has not fulfilled his obligation.
And this is difficult for me: shall the priestess be treated worse than the innkeeper?! With the more basic intention—understanding the words and listening to one’s own speech—after the fact, if he did not intend, he has fulfilled his obligation; but with the higher intention—fulfilling one’s obligation—according to the view that commandments do not require intention, he has fulfilled his obligation?