1) Even though Rosh Hashanah is the Day of Judgment, it is nevertheless a festival and the commandment of “And you shall rejoice on your festival” applies. It follows that one must eat and drink and be merry on it, as it says “Eat fat foods and drink sweet drinks… for the day is holy for our Master, and you should not be upset for the rejoicing of Hashem is your strength!”. (Shulchan Aruch and Mishne Berurah 597)
2) Even though one may not fast on Shabbos and Yom Tov even until midday, on Rosh Hashanah one may extend the prayers until after midday, and make Kiddush and eat afterwards. (Mishne Berurah and Kaf Hachaim ibid)