1) To explain why we don't blow shofar on Erev Rosh haShana, the Vilna Gaon in his commentary to Yonah (3:3) quotes the gemara (Gittin) that relates how Hashem sent a little bug or bird to fly up Titus' nose into his head and bang away there for years. One day Titus happened to walk past a blacksmith, and when the blacksmith's hammer was banging, the pecking in his brain stopped. Now finally having a way to get some relief, Titus arranged to have blacksmiths working in his palace, banging away day in and day out. After 30 days, however, the pecking resumed as usual. The bird had acclimated itself to the banging, and resumed its pecking at Titus brain.
You see from this gemara that when something happens for 30 straight days, a creature, whether it is a bird or a person, becomes acclimated to it and it makes no impression.
If we blew shofar inclusive of Erev Rosh haShana, then we would have 30 days of blowing before the chag and tekiyas shofar would make no impression on is. Tekiyos have to make a roshem! Therefore, says the GR"A, we take a break on Erev R"H.
(But we never have 30 straight days -- there are shabbosos in between that break things us? R' Chaim Kanievski points to the din that when you switch to saying tein tal u'mater, 30 days makes a chazakah and after 30 days you can assume in case of safeik that you said the correct insertion. Even though you don't say teil tal u'matar on shabbosos so the 30 days are really 26 days, the fact that the change at every possible opportunity to do so during those 30 days makes a chazakah. Same with teikyas shofar.)
אמרו לפני בראש השנה מלכיות זכרונות ושופרות מלכיות כדי שתמליכוני עליכם זכרונות כדי שיעלה זכרוניכם לפני לטובה ובמה בשופר
The kashe of ובמה is not asking "How do we properly fulfill the mitzvah of reciting malchiyos, etc." and telling us that you need to blow in the shmoneh esrei. The kashe the gemara is asking (see Ritva) is "How to we fulfill the mitzvah of coronating G-d as King?" And the answer is that you do that with a shofar.
That requires mental activity.
That requires the shofar making a roshem.
2) The Divrei Chaim of Sanz on our parsha quotes the pasuk in Yeshayahu 3:13 נִצָּ֥ב לָרִ֖יב הֹ׳ וְעֹמֵ֖ד לָדִ֥ין עַמִּֽים׃. The word נִצָּ֥ב there refers to Hashem standing in judgment, as Radak there explains, אמר אל תחשבו כי לא יענישכם האל על הרעות שתעשו כי בכל זמן הוא נצב ועומד לדין כל העמים כל שכן עמו ישראל We read in Tehillin 82:1 אֱֽלֹקים נִצָּ֥ב בַּעֲדַת־קל. The word "nitzvav" implies you are coming to pick a fight. אַתֶּ֨ם נִצָּבִ֤ים הַיּוֹם֙ כֻּלְּכֶ֔ם, we are נִצָּ֥ב לָרִ֖יב, to borrow the phrase from Yishayahu, we are troublesome, quarrelsome, rebellious. That's why we read the tochacha last week. Nonetheless, says the Divrei Chaim, we are לִפְנֵ֖י הֹ׳ אֱלֹקיכֶ֑ם, there is the shem Havaya, the midas haRachamim, that is extended to us b'pnimiyus of the din. This is what Rashi means:
התחיל משה מפייסן אתם ניצבים היום (דברים כ״ט:ט׳) – הרבה הכעסתם למקום ולא עשה אתכם כלייה, והרי אתם קיימים לפניו.
Despite הרבה הכעסתם למקום , despite אתם ניצבים היום, despite our rebellious quarrels, G-d does not punish us vindictively, and does not reject us. We are still הרי אתם קיימים לפניו and will always be so.