1) One of the 39 Avot Melachot (prohibited categories of activity) is kneading - ''Lisha''. Any action which involves binding together small particles (like flour), by means of a bonding agent (like water), to form one mass, might be prohibited on Shabbat, depending on the circumstances. Two common applications of this prohibition are mixing baby cereal with milk, or mixing eggs or tuna with oil. 2) There are two steps in the kneading process: adding the bonding agent (which alone causes some of the particles to bond), and then stirring the mixture; each of these acts is prohibited. Now, in general, when a ''melacha'' is performed in an unusual manner, although it's not considered a Biblical violation, the act is still prohibited rabbinically. The ''melacha'' of kneading, however, is an exception to this rule, and hence, it's permitted when performed using halachically specified modifications to the usual kneading process, such as stirring in a ''criss-cross'' fashion, rather than using a circular motion, or pouring from one vessel to another (see Shulchan Aruch 324:3).

1) The reason for this prohibition is that it's considered unnecessary exertion (Mishna Berurah 324:29). 2) According to the Aruch HaShulchan (324:2), any animal that one knows is hungry may be fed on Shabbat, even if it doesn't usually depend on humans for its food. 3) The Shabbat on which the public Torah reading includes the song sung by the Jews after the splitting of the Red Sea). 4) Others disagree and rule that this practice is permitted because it isn't exertion for the birds, but rather for ourselves. In other words, since we have a tradition that the birds sang along with the Jews at the Red Sea, we are throwing food to them out of gratitude, in order to remember the joy of the miracle (Aruch Hashulchan 324:3).

1) It's allowed to cook on a festival food that one will need on the festival itself, however one may not cook food on a festival for a meal afterwards. When one's cooking food for a festival, one may cook more than one needs in order to have left-overs afterthe festival, this is true only if it can all be achieved with the same act, for example, by merely adding extra pieces of meat to the pot. It's only allowed to cook on a festival for the sake of a Jew, but not for a Gentile (Shulchan Aruch 512:1); although it would be Biblically permissible to increase, on behalf of a Gentile, the amount of what's already being cooked for a Jew, the Sages prohibited doing this, out of concern that one might cook extra food for the Gentile alone. Furthermore, the Sages prohibited even inviting a Gentile to a festival meal, because people might end up cooking extra food specifically on behalf of the Gentile guest. 2) Since it's forbidden to cook anyway. 3) lit; idol worshippers. 4) And it's not considered an unnecessary burden, which is forbidden on Shabbat. See Chapter 82:9 for the laws of how to give food to a Gentile on Shabbat without coming to violate Shabbat prohibitions.