You guys have posted a lot of interesting hypotheticals! If I get any real work done today I'll go back and see if I can figure out the answers.
But basically, the 5th Amendment states "No person ... shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law." In the actual Miranda case (Miranda v. Arizona), the Supreme Court said police interrogation at the police station of a suspect in custody is by its nature coercive due to the power differential. Outside of people in law, most people wouldn't know they actually had a right to not talk. So, to "even the playing field," LE must warn suspects that: they have a right to remain silent, whatever they say can be used against them, they have a right to an attorney, and if they can't afford one an attorney will be provided for them.
Since then the Supreme Court has really limited Miranda. Miranda is a "prophylactic measure" designed to protect a suspect's 5th Amendment rights- which means the Court can limit it as it sees fit. A violation of Miranda isn't itself a Constitutional violation.
A smattering of recent cases have held that physical evidence found due to statements made in violation of Miranda is admissible, that statements made in violation of Miranda don't make later statements (after rights are read) automatically inadmissible, that statements made "off the cuff" before Miranda warnings are given are admissible as long as a reasonable person in the suspect's shoes wouldn't have thought he was in custody, etc.