Everyone within the borders of the United States has rights, even if they're here illegally. That's what it means to be a free country.
Calling ICE "gestapo" and Trump "Hitler" and are genuinely crazy things, gestapo can be pretty accurately described by 1984 as the thought police, ICE, while being an organ of a state is far from that. You may think they have immunity but federal courts seem quite fast at picking up the cases regarding the happenings in the article which I can assure you would not happen if ICE truly had immunity. And if ICE really was the gestapo, all the people at the protests and arrests would be killed indiscriminately; in the articles you see actions taking place before the shootings that can be seen as an attack on federal officers... If ICE was the gestapo just existing and showing you're against ICE would get you gunned down or arrested, it would get all the people at those protests gunned down or arrested.
I suppose Gestapo did have more menacing uniforms.
I'm not sure what you mean. The Gastapo was an organ of the state. Geheime Staatspolize means "Secret State Police."