1)
Why did they want to kill Yirmeyah?
1.
Malbim: They did not have any claim against him, just they did not want him to prophesize in the name of Hashem.
2)
They told Yirmeyah that they will kill him if he prophesizes. How could he say "va'Shem Hodi'ani
1.
Radak: He was not concerned for what they said in front of him. He thought that they merely scare and make empty threats. They could not kill him in public. To kill him covertly via poison was feasible. He would die only eight or 10 days later. People would not know that it is due to poison.