Do the people of Paradise go to Hell to bring out those in whose hearts they found faith when they intercede for them?

The Hadith referred to is authentic, and its apparent meaning is that the believers' request for intercession on behalf of their brethren occurs before entering Paradise and immediately after their salvation from Hellfire, as they say: "Our Lord, they used to fast with us, pray, and perform Hajj."

As for the Hadith of Abu Sa'id Al-Khudri, "Allah will admit the people of Paradise into Paradise... 'Look for whoever has in his heart the weight of a mustard seed of faith and take him out,'" the address here is to the angels, not to the people of Paradise, for the angels recognize them by signs that Allah grants them, such as the marks of prostration.

And assuming that the address is to the believers after they enter Paradise, this does not necessitate their departure from it. Rather, they have the ability to observe the people of Hellfire, address them, and intercede for them, as in His Almighty saying: "He said, 'Will you look down?' So he looked down and saw him in the midst of the Hellfire." The people of Paradise will not experience any fatigue therein, nor will they ever be expelled from it.