Using dairy and meat equipment

Hello, I have a few questions about what happens when parve food and equipment comes into contact with either meat or dairy equipment. 1) Chicken was made in a meat pot and rice was made in a parve pot. Then a meat spoon was used to take both chicken and rice out of their respective pots. Since the food was just made, it was all hot. Did the meat spoon make the parve pot meat? 2) If I make parve cookies in my dairy oven that was used to make cheese pizza within 24 hours, I cannot eat them with meat, but I can eat them after I have meat without having to wait. Is that right? Thank you very much for your answers!

1.In the case of the rice, using the meaty spoon taking out the rice does not make the rice pot meaty. However caution should be taken not to complicate things in the future. 2.In regard to eating your cookies baked in the dairy oven, you may eat the cookies after the meat meal as you said. Shana tova.