A custodial interrogation has been defined by the US Supreme Court as "questioning initiated by law enforcement officers after a person has been taken into custody or otherwise deprived of his freedom of action in any significant way." Your personal subjective view does not matter rather the standard is whether a reasonable person innocent of a crime would feel that they were not free to leave. If Miranda is violated only the statements obtained may be excluded i.e. the case likely won't get dismissed if other evidence exists.
Admissions you make to anybody can be used against you. Don't play lawyer, get a good criminal defense attorney.
The loss prevention officer is not a police officer, and you do not have the same constitutional protections. Any statements made to an LP officer will most likely be admissible against you.
The facts you mention with the police officer sound like you were in "custody" - as soon as a reasonable person would believe they could not leave, Miranda rights are required before proceeding with questions - handcuffs, police station etc are not the determining factor
The LP is not a police officer. Therefore Miranda does not apply to their conduct. Likewise the 4th amendment regarding searches and seizures does not apply to their conduct. In your scenario the arrest did not take place until the cuffs were put on and the person was told they were under arrest. The persons subjective belief that they were not free to leave is not relevant under Michigan law. Miranda and its rights are triggered by the actual arrest. Lastly, yes, statements made to the LP are admissible at trial.