1) On Succos we recite Hallel while holding the Lulav and Esrog and at different points of Hallel they are shaken. The poskim discuss the proper procedure in the event that one does not have a Lulav and Esrog in Shul. Does he (a) recite Hallel with the minyan and without the Lulav and Esrog and only afterwards take the daled minim, or (b) is it better for him to wait and recite the Hallel later b’yichidus (without the minyan) with the Lulav and Esrog. Harav Shmuel Kamanetzky shlit”a (Kovetz Halachos Succos page 372) maintains that one should recite Hallel with the minyan without the Lulav and Esrog (option a). However, Harav Gavriel Zinner shlit”a (Netai Gavriel Succos page 334) disagrees and he writes that it is better to recite Hallel with the Lulav even if that means reciting it without a minyan (option b). [See, however, Netai Gavriel on Daled Minim where he seems to agree with Harav Shmuel]
2) There are differences between those that pray Nusach Ashkenaz and those that pray Nusach Sefard as to when to shake the Lulav and Esrog in Hallel. Harav Shmuel Kamanetzky shlit”a (ibid. page 368) maintains that if one is praying in a shul that differs from his personal Nusach it is preferable to shake the Lulav and Esrog in accordance with the shul’s custom (and not his own). However, he concedes that the common custom seems to be that each person shakes them according to his personal custom regardless what shul he is in.