Regarding Tefilas Neilah – is it permissable for the Kohanim to duchen after shkiah?
In principle, one should try to ensure that birkas kohanim should be before shkiah (Mishnah Berurah 623:8). The Mishnah Berurah even writes that one should delay some of the piyutim, and say them after davening, to ensure that one makes it on time.
The Mishnah Berurah (Shaar Ha-Tzion 11) expresses doubt as to duchaning during bein ha-shmashos. The doubt is because there are opinions who permit duchaning at night, and even according to the majority who forbid it, bein ha-shmashos is possibly day.
Le-Maaseh, poskim are lenient, bedieved, up to 13 minutes after shkiah (Rav Shlomo Zalman and yibadel le-chayim Rav Elyashiv, see Piskei Teshuvos 623 note 13).