AFAIK, immigrants (whether legal or illegal) are in a gray area wrt constitutional protections. For example, on entry all aliens (including perm. residents) are fingerprinted whereas citizens are not. The lowly officer examining your papers can decide to not admit an alien into the country if you mouth off, and he's pretty much the final authority.
I seriously doubt any of things you describe are "problematic" from a constitutional point of view. It seems well-settled that aliens need not be treated the same as citizens.