1)
Why did he say "Asher Asah Lanu Es ha'Nefesh ha'Zos"?
1.
Radak: He swore similar to the matter. Yirmeyah said, you will kill me. Ha'Nefesh ha'Zos is what speaks, i.e. the Nefesh with the power of speech and Nevu'ah.
2.
Radak citing Targum Yonasan: Who sustained these souls.
2)
Why did he say "Im Amisecha v'Im Etencha b'Yad ha'Anashim"?
1.
Malbim: I will not kill you, and I will not give to these men [who want to kill you] to kill you.
