@boomerang,
If it can be authenticated, and if
Miranda rights have been waived, then yeah, it should be admissible (but there might be other things keeping it inadmissible, things like chain of custody and the like. Not everything that is possibly admissible, ends up being so). And sure, of course they're going to be figuring out what to ask you.
If suspect1 says to suspect2, "Don't tell my mom." Then the cops are going to lean on suspect1 with verbiage like, "Confess, and do your mother proud."
Miranda only really works when suspects keep their traps shut. Suspects/arrestees have few bargaining chips. And then they give this one away, so many times. This is cops taking advantage of trusting natures and a lack of preparation or knowledge.
I am not against the police, but things are so incredibly heavily weighted against people who are arrested. And nobody goes to a "What to do if you're arrested" class, either. People are scared, nervous, and they may even be guilty. A lot of the Reid Method takes advantage of the fact that most people will 'go along to get along'. Most people want to be liked. And they feel this way even if they've just knocked over a liquor store or sold a pound of heroin, too.
People who go to a police station for any purpose other something like reporting a stolen bike, or who talk to a cop who approaches them for anything more than a date or a cigarette should have their guard up. They should assume that whatever they say, and whatever they do, will be used, and that it won't be used to make them feel or look good.