Women are obligated by Torah law to recite Kiddush. Although women are exempt from all positive, time-bound Mitzvot (such as, Shofar, Lulav, Sukkah etc.) as we have explained on several different occasions, they are nevertheless biblically obligated to recite Kiddush, for inscribed on the first pair of Tablets (in Parashat Yitro) was the verse “Remember the day of Shabbat to sanctify it” while on the second pair of Tablets (in Parashat Va’etchanan), the verse “Guard the day of Shabbat to sanctify it” was inscribed on it. Our Sages explain that the words “Remember” (“Zachor”) and “Guard” (“Shamor”) were uttered in unison by Hashem in order to teach us that whoever is obligated in the “guarding” aspect of Shabbat, i.e. not to perform forbidden works on Shabbat, is obligated in the “remembrance” aspect of Shabbat, i.e. reciting Kiddush. Since women are likewise obligated to observe the Shabbat with all of its vast laws (since women are obligated to observe all negative Torah commandments, similar to eating on Yom Kippur), they are likewise obligated to recite Kiddush on Shabbat (see Berachot 20b). It is for this reason that women may recite Kiddush on behalf of men on Shabbat since both men and women share the same level of obligation when it comes to Kiddush. Nevertheless, out of concerns for modesty, it is improper for a woman to recite Kiddush on behalf of men unless those men are members of her household.
Since children who have not yet reached the age of Mitzvot (Bar/Bat Mitzvah) are not obligated to recite Kiddush on a Torah level, they cannot recite Kiddush on behalf of other adults who are obligated to recite Kiddush on a Torah level.
A blind man is obligated to perform all of the commandments of the Torah, in accordance with the opinion of the Sages (see Baba Kama 87a). Thus, a blind man may recite Kiddush on behalf of his entire household and they all fulfill their obligation in this way.
In the times of the Sages of the Talmud, wine was exceptionally strong and sharp and could not be consumed without first diluting it with some water. Thus, they would be obligated to first dilute the wine with water and only then could they recite Kiddush upon it. In our days, however, there is no obligation to dilute our wine. This is especially true with regards to grape juice since it is not strong at all. Nevertheless, Maran Rabbeinu Ovadia Yosef zt”l writes that it is preferable to dilute the wine with some water by pouring some drops of water into the wine three times; this should preferably be done when reciting Kiddush on grape juice as well. There is a deep Kabbalistic reason for this as Rabbeinu Yosef Haim zt”l writes in the name of the author of the Sefer Ma’avar Yabok. One should therefore dilute the wine by pouring in one drop of water three times. The dilution should be done right before beginning Kiddush, i.e. “Yom Ha’Shishi”, and not during the actual recitation of the Kiddush.