1)
Could people choose to go to the Bavliyim?
1.
Malbim: They did not let anyone leave the city. Only when they went to fight the Bavliyim, one who wanted to, he surrendered to them and remained there and did not return to the city - "Al ha'Kasdim."
2)
What is the meaning of "v'Haysah Lo Nafsho l'Shalal"?
1.
Rashi: Like one who plunders, he grabs and goes, so his soul will be seized from death, from the killers. Mahari Kara - saving his life will seem like plundering spoils (he will be elated, for he was sure that he would die - PF.)
2.
Malbim: His booty from the war is saving his soul.