yitzyshalom: Yet for followers of poskim who rule that it isn’t kosher, they will have the halachic status of being a mamzer. Even if another posek holds he/she isn’t a mamzer. See the Gemora in Yavamos that was mentioned earlier.
simcha613: Secular court shouldn’t be giving them anything. A Jew is prohibited from settling a dispute in secular court outside of beis din. Including in divorce matters. Going to arkayos is a tremendous sin.
Feif Un: Not according to the terms of the BDA Prenuptial Agreement. The BDA PNA mandates he must pay her $150 per day, every day, from the day she walks out of his home for any or no reason. Period. The terms are clear in black and white, as written and signed in the prenup. As long as they are not living together he must pay up, even if he has no halachic obligation to give a Get.