How probably is it that galaxies will extinguish? In the nebulaes of galaxies are stars born, but the gasses and dust they are made of comes from exploded stars (fe supernovas). So it looks like these processes can go on continuesly. But is that really the case, or does according to entropy(?) galaxies extinguish because fe the galaxie went too big so gravity has no opportunity to form other stars any more. And before colliding with other galaxies it is passed away. So is there any sign that galaxies are getting smaller or less active?
Galaxies are gradually being extinguished. Most star formation activity occurs near the start of a galaxy's life, or in response to merger activity with other galaxies.

The star formation rate of the universe peaked at redshifts of around 3, corresponding to a look-back time of around 9 billion years. Since then the star formation rate has declined as the universe expands; mergers are less frequent, gas is driven out of galaxies by supernovae and active galactic nuclei.

However, most of the stars that have been formed are of lower mass (K- and M-dwarfs) than the Sun and will live on for tens or hundreds of billions of years. They are however much fainter than the Sun. So although high-mass, luminous O- and B stars live their short lives and are not replaced at the same rate, the low-mass stars continue to shine. This means that galaxies will get fainter on average as the remaining stellar populations increase in average age and decrease in average mass.

It is a slow process though. High mass stars are still being formed in our galaxy after 12 billion years, and most spiral galaxies have ongoing star formation. However, star formation has more-or-less ceased in gas-poor elliptical galaxies.