Re: "This is a very confused post"
"What's at issue is whether ICE is itself breaking the law in enforcing other laws"
Any ICE agent that's been found breaking the law outside their remit has been processed accordingly. In terms of enforcing the law as it pertains the illegal aliens entering without permission to do so, hell I'd be happy if they were lined up and shot; but that would be unlawful. So they're lucky all they get is processed within the framework of the law itself.
"Every country in the world has some process for claiming asylum... [European Court of Human Rights ]"
Right, but again it's not the COUNTRY granting a guarantee of due process, it's a central EU court which is outside the country that has the ability to force that country to comply based on laws not of the country, but in the form of treaty. In the US, the court in question is a US court, making decisions based on US law.