Onion: Meat, Dairy, and Pareve
Question
Answer
Hello
Regarding the first part of the question: the onion fried in a pareve pot remains pareve. If it is then placed hot in a cold dairy pot, or if the onion is cold and placed in a hot pot, it will acquire a dairy taste.
However, if it is placed cold in a cold dairy pot, it will not become dairy.
Regarding the second part of the question: an onion fried or cooked in a pot of a certain type takes on the status of that pot, even if the pot was not 'ben yomo'. Therefore, if you cooked the onion in a meat pot, the onion becomes truly meat, and it is forbidden to eat it with milk. Similarly, if you cook it again in a pareve pot [as in your question], it will turn the pot into a meat pot.
When the first onion remains pareve, there is no problem cooking or mixing it later with a meat onion. However, if the first onion became dairy, it is forbidden to mix or cook it with a meat onion.
Source
Shulchan Aruch, Yoreh De'ah, Siman 95, Sif 2, and Siman 96, Sif 1