Suppose a star is 100 light-years away from the Earth. Therefore, the light coming from the star (which carries its information) takes roughly 100 years to reach Earth. However, if in the meantime the star dies, we would still be able to see that star in the sky. Is that truly right? If yes, how often does it happen when we look up in the sky (any guesses)?
Yes this is correct. However the kind of event you are thinking about rarely happens for stars in our Galaxy. The reason for this is that the size of our Galaxy is about 100,000 light years across, but the ages of most stars is measured in millions or billions of years. So, the travel time of the light to us is a tiny fraction of the stellar lifetime. For this event to occur, you need to see a star near the end of its life. Such an object is Betelgeuse in the constellation Orion. It is a massive supergiant that may be somewhere in the last 100,000 years of its life. It is however only about 700 light years away, so there is less than a 1% chance that this has already exploded and the light is on its way. It is however your best bet of seeing (with the naked eye) the progenitor of a star that is now dead.
If you go further afield though, to objects in other galaxies, then this issue does arise. Gamma ray bursts are thought to signal the deaths of very massive stars. They are seen in galaxies billions if light years away, but the lifetimes of the stars that produced them may have been a million years. In these cases we don't even see the long-dead star that exploded with big telescopes.
Somewhere in between we can see (with telescopes) the brightest massive stars in nearby other galaxies like that in Andromeda, at distances of millions of light years. Here, these stars are very likely to have already exploded as supernovae, as they have lifetimes of a few million years too, but we still see them "as they were".
Yes, as you said, the starlight we see from a star 100 light-years away was emitted 100 years ago, and yes, the star could have evolved into a white dwarf or gone supernova.
According to informal google research, in our galaxy, around 1 star per year "dies" (which usually means turns into a white dwarf). There are around 200 million visible stars in our galaxy, and around 200 billion in the whole galaxy, so the rate of star death amongst visible stars is about 1 star every 1000 years.
So, just for fun, if you stare at a star for 10 minutes, there is a 20 in a billion chance that the star you are staring at will have died while you were watching.
When we look at the stars, we are seeing them as they were years ago. If a star is 100 light years away, we are seeing it as it was 100 years ago, etc.
If a star dies (goes nova), we won't know about it for the year-equivalent of its distance in light-years. Then, one day, we'll see a flash in the sky and we'll know that if it is 27 light-years away, the star died 27 years ago.
That's exactly right.
Now, if you want to know "how often it happens", you'll have to be a bit more precise: do you want to know how many of the stars we can see today are already dead? or how many stars die on average on a certain period of time in the visible universe (i.e. that we will be able to watch die at some point)? or in the whole universe?
Also, you have to take into account stars that you can see explode, and stars that simply cool off.
I believe that you are correct in what you say. Because of the time it takes for the light to reach us here on Earth, we would be unable to know about the fate of that star, and the star would still be visible to us here on Earth, at least until the information of the star's end reaches us. I don't have any idea how often it happens. Maybe someone else has an answer to that?