I am very tired from the Rosh Hashanah prayers. It is very hard for me to wait for dinner of the second night of Rosh Hashanah until after the evening prayer. Can I eat the meal of the second night of Rosh Hashanah while still daytime after Plag Haminchah like we do when we accept Shabbat early on the long Fridays during the summer?

On the Second night of Rosh Hashanah and also on the night of the second Diaspora festival one should not make Kiddush (the sanctification of the Sabbath or a festival with a blessing over wine) until after nightfall after the evening prayer because the sanctity of the first festival is from the Torah. This is the law on the night of a festival which comes out on Saturday night because the sanctity of Shabbat is greater than that of the festival. Nevertheless if there is a great necessity such as for an elderly or ill person one should be lenient. See Rambam, Laws of Shabbat 29, 11. (שמירת שבת כהלכתה פרק מז סעיף כג ובהערה קיא). Regarding eating dinner before praying the evening prayers, note that according to the Kabbalists one should not make Kiddush before the evening prayers. The Maase Rav (117) writes that according to the Vilna Gaon one cannot make Kiddush before praying the evening prayers. The Kaf Hachaim (272, 3) writes that according to the Arizal one should first pray the evening prayers and then make Kiddush. The Mishnah Berurah (271, 11) however rules that if one wants to accept Shabbat (or a festival) while still daytime, make Kiddush and eat, and then pray the evening prayer he is allowed to, on condition that there is at least a half an hour before the time of the evening prayer.