The Seventh Day of Pesach (articles #1,2), is also a full-fledged Torah holiday; It celebrates the miracle of the Splitting of the Sea and our crossing on dry land.
The Eighth Day of Pesach, (#3) celebrated only outside of Israel. It's theme is the Final Redemption and Moshiach, as is explicitly discussed in the haftorah reading of the day.
Two are for the Torah Reading of Shemini on Shabbat, a major theme of which is Eating Kosher (5,6). Another, (#4) is for the seven weeks of Counting Omer,
and finally, the story (#7), leads to three different ideas discussed in the first Chapter of Pirkei Avot, which we start study this Shabbat afternon.