1. One should recite the “song of the sea” happily, and imagine that that day he himself had crossed the sea. One who says this song happily, has all of his sins forgiven. (Shulchan Aruch and Mishne Berurah 51)
2. The custom is to stand for Baruch Sheamar, Vayevarech Dovid, (until “Attah Hu Ha’Elokim”), and Yishtabach. On Shabbos it is correct to stand for the verse “Hashem melech, Hashem malach, Hashem yimloch le’olam va’ed” (ibid)