After a small star has burned through all of its fuel, it will enter a stage called the red giant phase. During this phase, the star will expand and become much brighter as it fuses heavier elements in its core.
Yes, eventually the star will run out of fuel completely and will no longer be able to sustain nuclear fusion. At this point, the star will collapse under its own gravity and either become a white dwarf, neutron star, or black hole.
The lifespan of a star depends on its initial mass. Smaller stars, like our sun, can burn for billions of years before running out of fuel. Larger stars, on the other hand, may only last a few million years.
During the main sequence phase, a small star primarily fuses hydrogen into helium. As the star evolves and runs out of hydrogen, it may fuse helium into carbon, oxygen, and other heavier elements. These elements are then released into space when the star dies.
If a small star has planets orbiting around it, they will likely be affected by the star's evolution. As the star expands into a red giant, it may engulf any nearby planets. If the planets are able to survive this phase, they may eventually be flung out of orbit or destroyed when the star dies.