Verse 13 said "va'Yishlach". Why does it say now "va'Yishlechu"?
Radak: This tells what happened at the end. Before he was given to Gedalyah, Nevuzaradan spoke with him. He found him among the exiles bound in chains like the other exiles, whom the Bavliyim bound. They entered the city and did not know anything that Nebuchadnetzar commanded about Yirmeyah, for he commanded [only] Nevuzaradan. The captors took him from Chatzer ha'Matarah, for he was there until Yerushalayim was captured, like it says above (38:28). Nevuzaradan and the other officers gave him to Gedalyah.
Malbim: The king sent Nevuzaradan and all officers of Bavel, and they sent messengers and took Yirmeyah, to take him out to the house. They gave to him a house to live in. He was also free, and dwelled among the nation as he desired.
Why did they give him to Gedalyah ben Achikam?
Rashi: He surrendered to the Bavliyim, like Yirmeyah told him. When the city was captured, they appointed him to rule over those who remained.
To which house did they bring him?
Radak: To the house where Gedalyah was.
Did he immediately dwell among the Am?
Radak: This was at the end, like it says below (40:6).