I was curious what is the source to recite Shalom Aleichem and Eishet Chayil as well as blessing children on Friday night. Also, what is the custom regarding special occasions (Shabbat and Yom-Tov, Chol Hamoed etc.)?
The source for the reciting of Shalom Aleichem is based upon the following passage in Masechet Shabbat 119b: R. Yose the son of R. Yehudah said: Two ministering angels accompany man on the eve of the Shabbat from the synagogue to his home, a good one and an evil one. When he arrives home and finds the candle burning, the table set and his bed made, the good angel exclaims, ‘May things be the same on the forthcoming Shabbat,’ and the evil angel unwillingly responds ‘amen’. But if not, the evil angel exclaims, ‘May things be the same on the forthcoming Shabbat,’ and the good angel unwillingly responds, ‘amen’. Thus by reciting Shalom Aleichem we are welcoming the good Angels into our home. The customs to say Eishet Chayil and to bless the children on Friday night, both have to do with the unique spiritual atmosphere prevalent the eve of Shabbat. In Kabblastic and Chassidic commentaries, the "Woman of Valor" refers to the divine presence or to Shabbat. By enumerating the virtues of the Eishet Chayil , we are in reality praising the virtues of Shabbat. There are various customs at to the reciting Shalom Aleichem and Eishet Chail on the eve of Yom Tov, Rav Tokachinsky zt"l in Luach Eretz Yisrael maintains that they are said. In regard to the blessing of the children, the Yavetz in his commentary on the siddur says that it is customary to bless the children upon the return from the synagogue for it is a time when there is an abundance of blessing and it is proper that this blessing bestowed upon the children.