In regard to burying on the second day of yom tov outside of Israel. Is it possible that there is a difference between the Gemara when the two days were really in doubt and today when the second day is minhag avot?
We could not find any such distinction in the Rishonim or Acharonim. It seems that there should be no reason to differentiate between the second day of Yom Tov when there was a real doubt concerning the day, and when the second day of Yom Tov is observed due to the Rabbinic decree of "continue to observe Minhag Avoseichem," (Beitzah 3b) because the very decree of the Rabanan was that we must observe the second day of Yom Tov in Chutz l'Aretz *just* the way our forebearers observed the day, that is, as a *doubt*.
(However, we must note that the RAMBAM indeed differentiates between our Yom Tov Sheni and the Yom Tov Sheni in the times of Chazal, regarding making an Eruv Tavshilin Al Tenai (Hilchos Yom Tov, 6:14), and he is actually *more stringent* regarding Yom Tov Sheni in our days than regarding Yom Tov Sheni in the times of Chazal when it was a real doubt. All of the Rishonim, though, object to this differentiation on the grounds that we mentioned above.)
Be well!