1) The parsha opens by telling us that Hashem could not lead the people through the land of the Plishtim פֶּֽן־יִנָּחֵ֥ם הָעָ֛ם בִּרְאֹתָ֥ם מִלְחָמָ֖ה וְשָׁ֥בוּ מִצְרָֽיְמָה, because they were not ready for war and might want to turn back to Egypt in fear. Instead, they went by way of Yam Suf, which necessitated splitting the sea.
Hashem always tries to minimize the amount of miracle required. The mashgiach R' Chatzel Levenstein asked: couldn't Hashem have just stiffened the people's resolve so that they would not fear the Plishtim and in this way they could take the shorter path? Wouldn't that have been easier than doing kri'as Yam Suf?
It must be, answered R' Chatzkel, that changing people's attitudes is in fact even harder than splitting the sea.
2) "There is no such thing as bad publicity," goes the saying. Some people love attention, no matter if it's for good or bad, no matter what the cost of that attention might be. I think that is the simplest pshat in this Midrash:
וַיְהִי בְּשַׁלַּח פַּרְעֹה – כְּשֶׁשָּׁלַח פַּרְעֹה אֶת הָעָם מִי צָוַח וַוי, פַּרְעֹה. מָשָׁל לְמֶלֶךְ שֶׁהָיָה בְּנוֹ הוֹלֵךְ לִמְדִינָה אַחַת, הָלַךְ וְשָׁרָה אֵצֶל עָשִׁיר אֶחָד וְקִבֵּל הֶעָשִׁיר בְּנוֹ שֶׁל מֶלֶךְ בְּעַיִן טוֹבָה, כֵּיוָן שֶׁשָּׁמַע הַמֶּלֶךְ מִי קִבֵּל בְּנוֹ וּבְאֵיזֶה מְדִינָה הוּא, הָיָה מְשַׁלֵּחַ אִגֶּרֶת אֵצֶל אוֹתוֹ הָאִישׁ וְאָמַר לוֹ שַׁלַּח אֶת בְּנִי פַּעַם אַחַת וּב׳ וְג׳ הָיָה מְשַׁלֵּחַ בְּכָל זְמַן וּבְכָל שָׁעָה וְשָׁעָה, עַד שֶׁהָלַךְ וְהוֹצִיא לִבְנוֹ בְּעַצְמוֹ, הִתְחִיל אוֹתוֹ הָאִישׁ צוֹעֵק עַל שֶׁיָּצָא בְּנוֹ שֶׁל מֶלֶךְ מִתּוֹךְ בֵּיתוֹ. אָמְרוּ לוֹ שְׁכֵנָיו לָמָּה אַתָּה צוֹעֵק, אָמַר לָהֶם כָּבוֹד הָיָה לִי כְּשֶׁהָיָה בְּנוֹ שֶׁל מֶלֶךְ אֶצְלִי שֶׁהָיָה הַמֶּלֶךְ כּוֹתֵב אִגֶּרֶת לִי, וְהָיָה זָקוּק לִי וְהָיִיתִי סָפוּן בְּפָנָיו, עַכְשָׁו שֶׁנִּמְשַׁךְ בְּנוֹ שֶׁל מֶלֶךְ מֵאֶצְלִי אֵינוֹ נִזְקָק לִי בְּדָבָר, לְכָךְ אֲנִי צוֹעֵק. כָּךְ אָמַר פַּרְעֹה, כְּשֶׁהָיוּ יִשְׂרָאֵל אֶצְלִי הָיָה הַקָּדוֹשׁ בָּרוּךְ הוּא זָקוּק לִי וְהָיִיתִי סָפוּן בְּפָנָיו וְהָיָה מְשַׁלֵּחַ לִי אִגֶּרֶת בְּכָל שָׁעָה וְאוֹמֵר: כֹּה אָמַר ה׳ אֱלֹהֵי הָעִבְרִים שַׁלַּח עַמִּי (שמות ט׳:א׳), וְהָיָה פַּרְעֹה שׁוֹמֵעַ מִפִּי משֶׁה שַׁלַּח אֶת בְּנִי וְלֹא הָיָה מְבַקֵּשׁ לְשַׁלְּחָם, כְּשֶׁיָּרַד הַקָּדוֹשׁ בָּרוּךְ הוּא לְמִצְרַיִם וְהוֹצִיא אֶת יִשְׂרָאֵל, שֶׁנֶּאֱמַר: וָאֵרֵד לְהַצִּילוֹ מִיַּד מִצְרַיִם (שמות ג׳:ח׳), הִתְחִיל פַּרְעֹה צוֹעֵק וַוי שֶׁשִּׁלַּחְתִּי אֶת יִשְׂרָאֵל, לְכָךְ נֶאֱמַר: וַיְהִי בְּשַׁלַּח פַּרְעֹה.
Pharoah regretted sending Bn"Y away because he missed getting that "אִגֶּרֶת" from Hashem on a regular basis in his mail. What was that אִגֶּרֶת? "Dear Pharoah, Release my people or you will get yet another makkah. Sincerely yours, G-d." And then the makkah would come. You would think a person would get tired of getting letters like that, of suffering one makkah after the next. Not Pharaoh. Better to have G-d's attention, to get his letters, even at the cost of makkos, than to be ignored. Such is the craving for attention.
We find something similar at the end of VaYechi, when the brothers return to Egypt after burying Yaakov, and we read (50:15)
וַיִּרְא֤וּ אֲחֵֽי־יוֹסֵף֙ כִּי־מֵ֣ת אֲבִיהֶ֔ם וַיֹּ֣אמְר֔וּ ל֥וּ יִשְׂטְמֵ֖נוּ יוֹסֵ֑ף וְהָשֵׁ֤ב יָשִׁיב֙ לָ֔נוּ אֵ֚ת כׇּל־הָ֣רָעָ֔ה אֲשֶׁ֥ר גָּמַ֖לְנוּ אֹתֽוֹ׃
Rashi explains מהו ויראו? הכירו במיתתו אצל יוסף, שהיו רגילין לסעוד עמו על שולחנו של יוסף, והיה מקרבן בשביל כבוד אביו, ומשמת יעקב לא קירבן.
Some of the meforshim (e.g. see Malbim, Ksva vhaKabbalah) learn that the word ל֥וּ here does not mean שמא ישטמנו, like Rashi explains, but rather הלואי. The brothers wanted Yosef to express whatever anger, whatever hatred, whatever bad feelings he may harbor against them. Why would they want such a thing? Because worse than suffering someone's anger is suffering being ignored.
Pharoah is like a celebrity whose moment in the sun has faded, and as much as they hated being hounded by media and fans in the past, they now miss the limelight. Pharoah exclaimed "Woe is me!" because worse than suffering G-d's makkos is suffering the fate of being ignored.
3) Even though Moshe told the people that "Hashem yilachem lachem" and they had nothing to fear, he paused and started to daven, as if he was less than confident of the outcome. Hashem immediately stopped him:
וַיֹּ֤אמֶר ה׳ אֶל־מֹשֶׁ֔ה מַה־תִּצְעַ֖ק אֵלָ֑י דַּבֵּ֥ר אֶל־בְּנֵי־יִשְׂרָאֵ֖ל וְיִסָּֽעוּ׃
וְאַתָּ֞ה הָרֵ֣ם אֶֽת־מַטְּךָ֗ וּנְטֵ֧ה אֶת־יָדְךָ֛ עַל־הַיָּ֖ם וּבְקָעֵ֑הוּ וְיָבֹ֧אוּ בְנֵֽי־יִשְׂרָאֵ֛ל בְּת֥וֹךְ הַיָּ֖ם בַּיַּבָּשָֽׁה׃
What was Moshe nervous about?
(Netziv writes that Moshe assumed that Hashem would save Bn"Y b'derech ha'teva. When things are done b'derech ha'teva, such as fighting a war, the overall outcome may be guaranteed, but there is no guarantee against harm to each individual. Therefore, Moshe davened.)
The Midrash comments on the pasuk וּבְנֵ֧י יִשְׂרָאֵ֛ל הָלְכ֥וּ בַיַּבָּשָׁ֖ה בְּת֣וֹךְ הַיָּ֑ם וְהַמַּ֤יִם לָהֶם֙ חֹמָ֔ה מִֽימִינָ֖ם וּמִשְּׂמֹאלָֽם that
היו מלאכי השרת תמהים לומר בני אדם עובדי עבודה זרה מהלכין ביבשה בתוך הים, ומנין שאף הים נתמלא עליהם חמה, שנאמר (שמות י״ד:כ״ט) והמים להם חמה אל תקרי חומה אלא חימה
When the malachim looked down at Bn"Y, they didn't see much difference between them and the Mitzrim. Why did Bn"Y deserve for the Yam to split for them and for the Mitzrim to drown?
Whether Moshe was aware of their thinking, or whether the same thought occurred to him independently, it clouded his judgment and led him to pause and question whether Bn"Y were deserving of the victory that was promised. It led him to think that without his tefilos, the Jewish people might not make it.
Hashem's response: וְאַתָּ֞ה הָרֵ֣ם אֶֽת־מַטְּךָ֗ וּנְטֵ֧ה אֶת־יָדְךָ֛ . You remember back in parshas Shmos, when Moshe was arguing with G-d about whether to accept his shlichus, Moshe questioned the faith of Bn"Y: וַיַּ֤עַן מֹשֶׁה֙ וַיֹּ֔אמֶר וְהֵן֙ לֹֽא־יַאֲמִ֣ינוּ לִ֔י וְלֹ֥א יִשְׁמְע֖וּ בְּקֹלִ֑י (4:1) Hashem responded by telling Moshe that he will give him signs to perform. First, to cast down his staff and it will turn into a snake. Rashi explains: רמז לו שספר לשון הרע על ישראל, ותפש אומנותו של נחש. Secondly, He told him to put his hand inside his cloak and it would turn white. Rashi explains: אף באות זה רמז שלשון הרע סיפר באומרו: לא יאמינו לי (שמות ד׳:א׳), לפיכך הלקהו בצרעת, כמו שלקתה מרים על לשון הרע Never cast aspersions on the Jewish people.
When the malachim began to voice their doubts, giving Moshe pause, Hashem reminded him of this lesson he learned on day #1 of his appointment as leader. וְאַתָּ֞ה הָרֵ֣ם אֶֽת־מַטְּךָ֗, pick up that staff that turned into a snake when you questioned the faith of Bn"Y; וּנְטֵ֧ה אֶת־יָדְךָ֛ stretch out your hand which turned white because you spoke lashon ha'ra against my people. How can you question the merits of the Jewish people compared to those of the Egyptians? (Techeiles Mordechai of the Maharasham).
Moshe's argument וְהֵן֙ לֹֽא־יַאֲמִ֣ינוּ לִ֔י וְלֹ֥א יִשְׁמְע֖וּ בְּקֹלִ֑י, was finally put to rest at Yam Suf, וַיַּֽאֲמִ֙ינוּ֙ בַּֽה׳ וּבְמֹשֶׁ֖ה עַבְדּֽוֹ׃.