Question: What are the special Halachot for when Purim falls on Motzei Shabbat?
1. Bringing the Megillah to Shul on Shabbat: We do not read the Megillah when Purim falls on Shabbat (though nowadays only Shushan Purim can fall on Shabbat). This was decreed in order to prevent people from carrying the Megillah into a public domain (which is forbidden on Shabbat). There are later authorities who forbid carrying the Megillah on Shabbat even within a private domain on account of it being Muktzeh (something that may not be moved on Shabbat), but most authorities disagree and permit it (Shulchan Aruch Orach Chaim 688 and Mishnah Berurah #18). There is, however, a problem with bringing the Megillah to Shul on Shabbat when Purim falls on the next day because of the prohibition of preparing on Shabbat for a weekday. If one does bring the Megillah to Shul on Shabbat, it should be brought inconspicuously, and one should be sure to learn something from it at Shul on Shabbat itself (Kitzur Shulchan Aruch 141:17. Aruch Ha-Shulchan, Orach Chaim 693:3).
And it is permissible on Shabbat to prepare for reading the Megillah. It is not considered preparing on Shabbat for a weekday, since it is learning Torah (Shemirat Shabbat Ke-Hilchata Chapter 28 note #169).
2. Children Dressing in Purim Costumes on Shabbat: Children may dress up in a costume on Shabbat before they come to Shul, since they will have enjoyment from the costume on Shabbat itself. It is therefore not considered as if one were preparing on Shabbat for a weekday. This is obviously on the condition that there is no part of the costume which is Muktzeh, and it does not involve painting, [forbidden] tying, and other similarly forbidden things. Adults, however, may not wear costumes on Shabbat, since many authorities rule that it is preparing on Shabbat for a weekday (Shalmei Todah - Purim of Rav Pelman #42. Kaf Ha-Chaim 529:3, 551:93). And it is also not honoring Shabbat.
3. Noisemakers on Shabbat: Noisemakers are definitely forbidden on account of Muktzeh. And even if they are not Muktzeh, one may not bring them because of preparing on Shabbat for a weekday, since one cannot rely on the solution of using them on Shabbat itself, as making noise from any type of instrument, object, etc. on Shabbat is forbidden (Kitzur Shulchan Aruch 80:87).
Summary: It is permissible to bring a Megillah to Shul while it is still daytime on Shabbat, provided that one learns something from it. It is permissible for children to dress up in a costume while it is still day time, but it is forbidden to bring noisemakers.