Q. 2) See question above: (Since it is an ancient tradition that on Shabbat Shira you feed the birds) In our particular case, is it permitted to have the kids come together and feed our birds inside the cage?
A. Shulchan Aruch (324: 11) permits feeding during Shabbos one’s domesticated birds that one is obligated to feed.
Biur Halacha (ibid.) mentions that others may also feed those birds.
Therefore, you may indeed permit the children to gather on Shabbos Shira and feed the birds.
Horav Shlomo Miller’s opinion is that one should be careful to throw the seeds through the bars or grid of the cage, and to not open the gate or door to it, since one may not be permitted then to close it on Shabbos, The reason being that if left open, it would allow the birds to escape. Therefore, closing it would comprise trapping or the Melacha of Tzod. (Shulchan Aruch O.H. 316: 7).
Rabbi A. Bartfeld as advised by Horav Shlomo Miller, Horav Dovid Pam and Horav Aharon Miller Shlit’a