To the question “Are the stars we see really there?”, there is a simple, if non-committal, answer: maybe.
We see things when light is either emitted by something and it reaches our eyes, or else, light is reflected off something and it reaches our eyes.
Stars are basically giant balls of gas that is fusing together to form heavier elements. In the process they emit light. This is very much like our own sun operates: hydrogen fusing to create helium, and giving off a lot of heat and light in the process. Heat, in the form of infra red radiation can be detected by special equipment, but it is the light we are interested in: because this is what we can ‘see’.
However, when all the ‘fuel’ has run out, the star can do one of many things, for example: die out with a whimper, die out with a massive ‘supernova’ explosion or collapse in on itself and start another heavier chain of nuclear fusion as a new set of life.
During all that while, stars emit energy in the form of electromagnetic radiation. Very often, this lies is in a frequency spectrum in the visible range. Less technically speaking, many stars emit life while their fuel reacts.
And then, you must add up the fact that most stars are very, very far away. They can be billions, trillions, or quadrillions of kilometers away from us, or often even further. In fact, we have still not determined the ‘furthest’ star’s distance. Light, travelling at about 299,792.458 km/s (or in units one can more easily relate to, about 1,079,000,000 km/hour), can take months, years, decades, centuries, or more to reach us. This is so significant that astronomers often measure large distances in light-years: the distance light travels in exactly one year.
In that time, however, the star may have died. Alternatively, it may still be alive and burning away.
There are however, very advanced analysis techniques that allow scientists to at least give a percentage probability of the star’s current presence. This is based on the current condition of the star, the distance of the star and stability of the fusion fuel of the star, amongst other details.
Think of it this way: if a mailman takes a letter of identification from Peter yesterday and takes one day to reach you. He reaches you today. Right now, you do not know if Peter is still alive or dead, but he certainly was when he sent that letter.
It is much the same story with stars. So, are the stars we see really there? Perhaps. We don’t really know for sure.