There are several things we don't do in order "to confuse the Satan", like not blowing Shofar on Erev Rosh Hashana. How does it help? Does Satan not realize that Rosh Hashana didn't pass yet? He doesn't see our calendars?
Rashi explains the concept of "confounding Satan" as follows: "So that he will not accuse; for when he hears how the Jewish people love the mitzvos, his words of accusation are stifled."
Essentially, our blowing shofar in different ways (sitting, standing, tekieah, shevarim, etc..), shows our love for the mitzvos and this causes the words of Satan to be suppressed.
We are not trying to confuse Satan about the calendrical day of Rosh Hashana, but-
rather, it means that Satan won't know when the specific aspect of the period of judgment of Rosh HaShanah comes about - the point of time when he presents his accusations. This is stated explicitly in the Maharil: "He does not know when is the time of judgment; when he is to come and accuse."
When a Jew repents properly prior to the onset of Rosh HaShanah, then he is already assured that he will be written and sealed in the Book of the Righteous. In other words, by repenting prior to Rosh HaShanah, his judgment for the good was already assured during the month of Elul.
So Satan sees his efforts are useless; we stopped blowing shofar even before Rosh Hashana, because we have already been forgiven, and this confounds his presentation in the Heavenly Court, because he sees that "כבר עבר ר״ה" - "Rosh Hashana already occurred". Not the day of Rosh Hashana, but the judgement of Rosh Hashana.
I would assume that the other minhagim that "confuse" Satan, are of the same sort - showing our confidence that we have already been written and sealed for a good, sweet year, filled with all good things.
It is said in the name of Rabbi Akiva Eiger as follows:
The Talmud states that if one repents due to fear of punishment, his sins are converted to unintentional sins. However, if one repents out of love, his sins are converted to Mitzvoth (good deeds).
Rashi states that the extra shofar blasts show the love Jews have for Mitzvoth, this implies that their repentance is motivated by love rather than fear. Accordingly, their sins would be converted to Mitzvoth.
Satan is thus in a quandary: for every sin he brings up against the Jews, is subject to possible conversion to a good deed, which moves Hashem to shower blessing upon the Jews, the opposite of Satan's goal. When he hears the shofar blasts he gets confused and doesn't know how to proceed.
I remember reading a drasha by Rabbi Chaim Smulevitz who gave an answer why we blow the shofar multiple times on Rosh Hashanah.
He said at the first blast the Satan prepares his arguments for the Day of Judgement. When he hears the second blast he assumes that Moshiach has now come and this agitates him so much he cannot deliver his accusations.
Is the Satan so foolish he is tricked every year with the same trick? Rabbi Shmulevitz says that the Satan is far more aware than we are of how close Moshiach is to coming. The teshuvah that the Jewish People need to do to bring Moshiach is something intimately close to them and requires in essence just a change of thinking. Knowing that, the Satan expects the Shofar HaGadol to blow at any moment.
Nachum Klafter recently posted an essay on Torah Musings proposing an answer to this question.
Read the whole thing, but in summary:
He suggests that the Satan here is our own evil inclination, and in particular, our unfortunate tendency to strip meaningful practices of their meaning by practicing them in a rote manner. As we've been blowing shofar for a whole month, we may naturally tend to adopt an automatic feeling toward the shofar blowing and the repentance it's supposed to inspire. We break the routine before the big event to vanquish this particular evil inclination and instead concentrate properly on the shofar and its meaning.
"Judaism does not view the word “Satan” with the same connotation as other religions. Satan in Judaism is not a physical being, ruling the underworld or hell. Rather, in the Torah, the word Satan indicates “accuser,” “hinderer,” or “tempter.” Satan is more an obstacle in one’s way, such as temptation and evil doings, keeping them from completing the responsibilities of tikkun olam (fixing the world). Satan is our evil inclination to veer off the path of righteousness and faithfulness in G-d.
The Shofar is a wake-up call, a remind er that one wil hear and do all that HaShem commanded. So this could confuse or shaken up our yetzer hara and the drives that keeping us from this goal in order to get us back focused on the right track.