How do astronomers know when the Sun will die? How it is possible for astronomers to find out when the end of the Sun's life will be?
Yes, astronomers could be wrong.  Part of being a scientist is always having to be ready to admit that you were wrong.

Astronomers have developed models of how the sun and other stars work. We understand them to be nuclear furnaces. These models may not be perfect, but they are well supported by the evidence and can predict much of what we observe from the sun and other stars.

Using these models we can expect the sun to exist for about 10 billion years, and it is currently about 4.7 billion years old. While the model could be wrong, it is probably not very wrong, and the sun will go on shining for a long time yet.