Only the stars that explode into supernovas can go on to make new stars. When they explode, all the atoms that made them up get scattered into a huge cloud of gas and dust, and then over a long time, gravity attracts particle to one another, and slowly you can build up enough to make a new star.
The ‘sword’ hanging down from Orion’s belt is actually a big cloud of gas where new stars are forming right now. The whole process can take millions of years.
We call “shooting stars” that because they sometimes look like stars falling out of the sky, but really they’re very different things. “Shooting stars” are meteorites – tiny particles of dust or rock burning up in our atmosphere. The stars are much much bigger and much much further away.
For both things though life is a one way process. Once the shooting star has burned up it’s gone. And once a star dies it’s dead – although some of them have very long lives as “stellar remnmants” like white dwarfs, neutron stars or black holes.
Stars aren’t strictly re-born: they can die, explode, and produce material to make another star, often smaller I would expect than the one that exploded.
To get a new star from an exploded one would take at least 100 million years, I’d guess. Actually, I’m not sure how long our Sun took to be formed turns out that it could be as quick as 30 million years for a Sun-sized star to start contracting, form a protostar, and then begin nuclear reactions that keep it from contracting anymore and turn into a proper star.
In context, 30 million years ago on Earth, life wasn’t that different from now. So 30 million years is quite quick.
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