Why do so many professional singers sound off-key on live TV performances?
I'm a professional singer, if that gives my answer any weight. It's because the sound is entirely different on a TV sound stage then it is in concert. There are no main speakers, just stage monitors, and ususally really crappy ones. It's not just that it's hard to hear, it's also that the sound you are hearing is very different to the sound in concert, much flatter and drier, actually quite dead compared to a stage. This is critical because, unless you are one of the few blessed with perfect pitch (you're either born with it or not) you need to hear yourself well, and hear the band well, to help you find the correct pitch. When the sound isn't right, and it usually isn't on tv, then the singer has to make guesses and assumptions on what everyone is sounding like, and that often leads to a perfectly good singer being slightly off pitch with everyone else in the band. Now, sometimes it's simply because they were never good singers to start with, but fixed their flaws in the recording studio with technology. That happens all the time. But even the best singer, if they don't have perfect pitch, can go flat when they can't hear well.
I want to be a professional and famous singer but,?
You just need lessons and practice. Almost all professionals begin with minimal musical ability. Some amazing singers started out a disaster when they first started singing. Despite what much of the public assumes, singing voices can be extensively trained to be beautiful, even if you're less than impressive to begin with. Singing is a very anatomical process - a qualified vocal coach would be able to evaluate you, figure out what's holding your voice back, and begin a training routine that changes weak sounds into strong, beautiful ones. No drastic results will happen overnight, but if you have patience, you will improve. We all have a hidden potential that just needs to be unlocked.