For the point mentioned, "On hag Pesach, if one finds rice in a cooking pot, the rice can be removed and the food eaten," Rav Ovadia in Yechaveh Daat 1:10 brings Achronim who say that the Rema in OC Siman 453:1 says that even for those who have the minhag to not eat rice on Pesach and rice falls in a pot of food it's not assur bedieved and the poskim say one can rely on batel bashishim and even more than 60 (the Chok Yaakov, Eliyah Rabah there, and Shu"t Zera Emet 3:48 also agree).
For the point, "Does that mean one can cook rice in a pesadik pot before Pesach?" In Shu"t Zera Emet 3:48 he says that an Ashkenazi can cook in a vessel in which rice or kitniyot was cooked in bedieved (the Kaf Hachaim OC 453 Seif Katan 27 agrees). This would apply to Pesach and all the more so before Pesach. According to the Piskei Teshuvot 453:9 and Ulehorot Natan 15:14, one should lechatchila not use a utensil on the same day (within 24 hours) that kitniyot was cooked (בן יומו), however if one does use that vessel to cook other food, one can eat that food bedieved. This applies to Pesach and all the more so before. In Chazon Ovadia Pesach Page 86 he writes the same thing.
Link used: https://www.yeshiva.org.il/ask/132083
Hope this makes sense