1) One is allowed to exert oneself to alleviate discomfort, but not to increase the comfort level of the animal, because it's considered unnecessary exertion. 2) Shulchan Aruch 305:10.

1) One of the 39 ''Avot melachot'' (prohibited categories of activity on Shabbat) is planting - ''Zoreah''. This category covers any activity that enhances growth, therefore, throwing seeds, on Shabbat, into an area in which they may potentially sprout is prohibited. The Shulchan Aruch (336:4) permits throwing grains to fowl if the grains will be totally consumed within two days, because it takes at least 3 days for grains to sprout. Furthermore, the Shulchan Aruch permits throwing these grains into an area where people walk, because the grains will not sprout in that sort of environment.

1) One of the 39 ''Avot melachot'' (prohibited categories of activity on Shabbat) is ''sifting'' - ''Meraked''. Since one usually wouldn't remove chaff from hay with a sieve, doing so wouldn't be a violation of a biblical prohibition. However, since it's similar to the ''melacha'' of sifting, the sages prohibited it (Mishna Berurah 324:1 and Sha'ar Hatziyun). The Aruch Hashulchan (324:5), however, rules that this would be a violation of the biblical prohibition against sifting. 2) This is true even though some of the chaff may fall away through the holes in the sieve. Since one's intention is not for the chaff to fall away, it's permitted. In general, even if the performance of a ''melacha'' may occur as a result of a particular action, as long as it is not inevitable - ''Psik Reisha''- and one's purpose isn't to perform the ''melacha'', the action is permitted. In this case, the Aruch Hashulchan 324:5 explains that although some chaff might fall away, a large amount will remain in the sieve, and hence, it does not constitute a ''Psik Reisha''.