1) Although the Shulchan Aruch writes to eat a minimum of a K'zayis (Food amount equivalent to the size of a half or a third of an egg) at the Melave Malka, it's best to actually eat a little more than a K'Beitaza (Approximately double the size of a K'zayis) in order to establish it as a meal, a Kvias Seuda. (See Machtzis HaShekel Siman 291:1)

Furthermore, some Poskim write that in order to establish it as a meal, the table should be set with Lechem Mishneh (two complete loaves of bread), although only one of them should be lifted and used, as there is no actual obligation of Lechem Mishneh at Melave Malka. (See Kaf HaChaim Siman 300:5)

2) Many scrupulous people make sure to eat hot bread at the Melave Malka meal, as the Talmud (Shabbos 119b) says that eating or drinking something hot, especially hot bread, at Melave Malka is a Refuah (cure) for the body. Additionally, many Seforim write that it's a Refuah for the Neshama as well. (See the MaHarsha to Shabbos 119b where he explains that by eating something that was warmed up after Shabbos we honor the Shabbos by showing that we were unable to cook on Shabbos.)

If one cannot eat hot bread, drinking something hot can suffice. (Ruling of Rav Yaakov Emden Zatzal in his siddur. See also Rashi Shabbos 119 b Dibur Hamaschil Chamin)