Below is an image of Supernova remnant G1.9+0.3:
This supernova is located ~27,000 light years away from Earth, meaning that it takes at least 27,000 years for the light from this supernova to reach Earth. Try making any kind of scientific sense out of that with the assumption of a 6,000 year old universe.
But wait! It gets worse. This is a supernova, meaning that it is the remnants of an exploded star. Stars have very long lifespans. The largest stars have the shortest lifespans--as little as 10 million years, while smaller stars can last for around 10 billion years. So how did we get a supernova remnant from a dead star whose light takes over 27,000 years to reach us in a universe that is only 6,000 years old?
Your claim about how old stars are is based entirely on theory, not observational science. There are actually quite a few alternative theories all of which are quite valid scientifically but that aren't main stream and so get ignored. The point being that we do not actually know for a fact how long stars last or even what powers them.
As for the distance to distant objects, we don't really know that either. Red shift theory is in real trouble and has been for decades. Main stream science mostly just ignores the problems with it and just keeps on going as though the problems don't exist.There are some who try to explain the issue away but they typically are nothing other than ad hoc rescue devices (i.e. they aren't scientific).
"On October 3, 2003, the Big Bang theory was falsified by direct observation. The galaxy NGC 7319 was measured to have a redshift of z = 0.0225. It is not uncommon for “nearby” galaxies to have redshifts below z = 1. However, a quasar was located in front of NGC 7319’s opaque gas clouds with an observed redshift of z = 2.114.
The two principle tenets of the Big Bang theory are that redshift is proportional to distance and that it is an indicator of velocity. The larger an object’s redshift the farther away it is and the faster it is moving away from the observer. Those two ideas provide the backdrop for the commonly held belief that the Universe is expanding.
According to the Big Bang, the NGC 7319 quasar “must be billions of light years farther away than the galaxy” because it has a higher redshift. Yet, since the galaxy is opaque, the quasar has to be in front of the galactic dust clouds and not shining through them.
“No one has found a quasar with such a high redshift, with a redshift of 2.11, so close to the center of an active galaxy,” said the late astronomer Geoffrey Burbidge at the time. The discovery team included his spouse, E. Margaret Burbidge, another noted astronomer. The find was significant because it is the most extreme example of a quasar in front of a galaxy with a lower redshift." - Stephen Smith
The above is by no means the only such example. There are dozens, perhaps hundreds. The unfortunate fact is that there isn't any way we know of for us to tell how far away these object are once they get passed the point where we can measure their parallax.
The bottom line is that the things you think you know are not the facts that modern science presents them to be. Evolution, whether cosmological or biological has become a religion and most of main stream science left the actual scientific method behind about a hundred years ago and trading observation with mathematical abstractions and computer models.