You don't have the right to remain silent. You have the right not to be compelled to provide incriminating testimony. The cops have the right to ask you questions otherwise.
Um, the first line in the Miranda warning literally says you have the right to remain silent. That is for police questioning, which they can choose to do whether you answer or not. The fifth really won't come into play until sometime around being charged and questioned by a judge and/or prosecutor.
The Miranda warning is layman's explanation of the right. It does not define the right itself. For example, if the police rush to the scene and A claims that B hit her, they can ask you "did you see B hit A?" and you don't have a right to stay silent.
The "right to remain silent" that is in the Miranda warning, laymen explanation or not, is in effect when you are under arrest and face police questioning. That is the situation that I'm referring to and your example is a completely different context.
Although I would be curious as to the legalities as to a police officer having the ability to force an answer to a situation you are not directly involved with. A classic example is compelling testimony when you are a witness and your life has been threatened if you do give testimony. In those cases I know you have no right to be silent, you can be punished for doing so. But that's in a court of law and a cop asking you a question over the matter at the scene is an interesting variable. I suppose the cop could arrest you for obstruction of justice, but then the Miranda warning would then be in effect.
I'm not sure what you mean here. In that case, you could be arrested as a material witness and compelled to testify, but if there's any chance that a statement on the matter could incriminate yourself, wouldn't you have to be granted immunity first?
Because you also have the right not to remain silent. Explicitly invoking it makes it clear to all involved, and helps you out if they keep you awake for 36 hours and keep asking in hopes you get worn down.