Q. Dear Rabbi, Are the branches decorating the Shul Muktzeh, if they fall down, or can you remove them on Yom Tov?

Decorative branches that were placed on the Shul before Yom Tov are not Muktze. See Mishna Berura (494 – 9) in the name of the Mogen Avrohom. Mishnas Yaakov (ibid.) writes that he observed Torah sages that moved those branches as they went up to the bimah. Horav Shlomo Miller Shlit”a opinion is that if they were only fixed temporarily and can easily be removed, they are not Muktze.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a