A witness who testifies to the content of a conversation where they were a participant is not generally regarded as hearsay, though the conversation reported is not presumptive evidence that statements made in the conversation were factual, or true. In effect a witness is testifying only to the words, and not the truth or falisity of them. There are also safe guards intended to insure that the conversation testified to is accurate and did take place as described.
The situation you've described is hearsay if the sole purpose for stating the words of the other participant to the conversation is to prove the truth of what was stated. Thus, if Witness testifies that Stranger said, "Defendant ran a red light," and the purpose for testifying is to prove that, in fact, Defendant ran the red light, it would be hearsay, and probably excluded unless an exception to the Hearsay Rule applies. If the purpose is not to prove that Defendant ran the red light, but merely to prove that Victim said those words, then it's not hearsay.
True hearsay is when a witness tries to testify to second-hand knowledge of a conversation. "Mrs. Jones told me that Mr. Doe admitted....". That sort of testimony is excluded.
This circumstance is hearsay, but it is hearsay within hearsay.
A notable exception is the dying statement. In that case, a person on their death bed (or believing that they were on their death bed) may make statements that can later be introduced in court by the person(s) overhearing the statements. For instance, a badly wounded robbery suspect believing they are about to die mutters to the attending physician that he and James Doe murdered a guy named Joe Schmoe in '96. The bandit dies and Jimmy Doe is charged with the murder of Mr. Schmoe, whose homicide had previously remained unsolved. The dead bandit's comments would be treated as a dying declaration, and would be a center piece to the prosecution's case against Mr. Doe. Of course, other physical and circumstantial evidence would be needed for conviction.
Yes; This is the "dying declaration" exception to the Hearsay Rule. Possibly also admitted as an "admission against interest."