And there are stars being “born” and dying all of the time. You don’t notice it because there are thousands of stars in our limited field of view, and they are relatively stable… as in.. they won’t be blowing up any time soon.
And you actually can see new stars if you look in the Orion Nebula. Look up at the sky and find Orion’s Belt, and then his sword which is somewhat perpendicular to the belt. The middle “star” of the sword is actually a star forming nebula.
The expansion of the universe is something different. It has nothing to do with how many stars we see in the sky because the scale is so big that it’s not even on the star scale of movement. When they say the universe is expanding it’s because from measurements it’s been shown that nearly all other galaxies are moving away from us and at an accelerated rate.
(there are a few moving nearer to us, because they are in the same “local” area and we are basically orbiting one another.)