Pesachim 114: Getting Everything in Order (It's the Seder!)

It's the seder! First, the first cup, for kiddush. What should the order of the blessings be? [What's What: Tadir ve-she'aino tadir] Note that the dispute here is between Beit Shammai and Beit Hillel, where we have a given (from a bat kol, no less) that we always pasken like Beit Hillel. Which the Gemara acknowledges here as well, perhaps redundantly. Continuing along with the seder... the vegetable, the matzah, maror, haroset. Plus, the confluence of maror and karpas - suggesting that mitzvot require intent to be fulfilled. Except that mitzvot do not need intent. So how do we make sure maror is maror, and that karpas doesn't fulfill the maror obligation? Also, the examples of the cooked foods for the seder include... rice!