Shalom Aleichem and Eshet Chayil on Shabat Chol Hamoed

I would like to know what the custom is for not reciting both Shalom Aleichem and Eshet Chayil on Friday night of Chol Hamoed... Also do we know when the Hagadah was officially compiled (what year?) and who put the Hagada together? And lastly why is the Kabalat Shabat on Yom Tov and Chol Hamoed shortened when we have the Tadir Vesheono Tadir - Tadir Kodem principal?

1. I believe the common custom is to recite Shalom Aleichem and Eishet Chayil on Chol Hamoed and Yom tov, with the exception of the Seder night, when we want to start the Seder as early as possible so the small children won't be tired or bored. 2. The basic format of the Hagadah is foung in the mishna, and the main body of the text was finalized in the time of the Geonim (before the 9th century) 3. The principle of "Tadir Vesheaino Tadir" applies to the order of things if we are doing both. On Yom Tov we basically have the Yom Tov service with additions for Shabbat, instead of the other way around. The Kabbalat Shabbat, comprised of 6 chapters of Tehilim, "Lecha Dodi", and the psalm for Shabbat, represents the transition from the weekdays to Shabbat. On Chol Hamoed or directly after a Yom Tov the transition is not so abrupt, hence the shortened version.