"do those individuals that have illegally settled into our own Nation, enjoy the same protections under our own Constitution, or not?"
As I stated before the Constitution protects them roughly similarly to non-citizens that are here legally.  The fact that they committed a crime does not change the limitations on government action under the Constitution.
"The fact that they are here illegally, first and foremost, does, and should not, afford them said protection within our own Constitution"
You are still thinking about the Constitution in the wrong way.  The Constitution does not grant or bestow protections, ie. produce positive rights.  It limits government action, ie. produces negative restrictions.  For example, there is no right to privacy under the words of the Constitution.  It is not specifically "granted" or "bestowed."  However, the limitations on government actions in other areas, e.g. protection from unreasonable search/seizure, grounds such substantive due process rights.