There is only 1 universe it is all encompassing and never ending (size not time). if you are referring to the idea of multiple dimensions of reality or in other words a "parallel universe" then you're also somewhat mistaken as they are all happening in real time and at the same time, just the outcomes of events are different. the theory goes like this: in universe A you are a veterinarian but in universe B you could be the president of a country. Basically your age doesn't change only the world events change from dimension to dimension. (or so the theory goes) the idea of you always being alive in 1 of them is near 0.
I personally only believe in what can be proven. I am a realist.
Well, the idea was created to negate the need for an observer for quantum decisions. The idea is for every quantum decision (which is seen as a probability of different events happening), each possible event happens in a different world (hence the name, Many Worlds Interpretation). If this doesn't happen, then the Universe is in a constant state of superposition, undecided, if you will, until it is observed by a consciousness. This doesn't really ring true for me, so I tend to believe the Many Worlds Interpretation.
Quantum Immortality is a theoretical extension of that, which says that when you're about to die, there will be a small, but finite possibility that you will live instead. Since this is a possibility, it must happen in one of the many worlds. For example, if you were shot, there's an extremely small possibility that the bullet will quantum tunnel through your head and to the other side, leaving you unharmed. Since this is a remote, but real possibility, it will be realized in at least one of the other worlds. Rinse and repeat for every time you're about to die, and you get Quantum Immortality.