Do I understand correct that there is one placed called "Hell" and another place called "Hades"? And Hades is where the souls of the dead go until the final day of judgement?
The term Hades is a general reference to "the realm of the dead". By itself it means nothing about what happens there. Based on the description given by Jesus in Luke 16:19-3, it makes sense to say that Hades has two zones, a place of torment and the "bosom of Abraham." I believe that the bosom of Abraham is another way of saying the "paradise" that Jesus mentioned to the thief on the cross in Luke 23:43.
For the torment part, this is not the same as the final hell which is also called the lake that burns with fire in Revelation 20:13-15, "And the dead were judged by what was written in the books, according to what they had done. And the sea gave up the dead who were in it, Death and Hades gave up the dead who were in them, and they were judged, each one of them, according to what they had done. Then Death and Hades were thrown into the lake of fire. This is the second death, the lake of fire. And if anyone's name was not found written in the book of life, he was thrown into the lake of fire." Since Hades will be thrown into the lake, it would not make sense to believe that Hell and Hades are the same place.
In the story that Jesus relates in Luke 16, the rich man had relatives still living, so he could not have been speaking of a time after the end of the world. The rich man also asked for Lazarus to do things, so I would assume that means that Lazarus was also conscious. There are other passages that would suggest that the dead wait in a sleeping state like I Corinthians 15:51. I personally think that Corinthians could be using some poetic license, so I favor thinking of what Jesus said in Luke to be an easier description to understand.
Some people would like Luke 16 to just be a made-up story so that Jesus can express a point. However, if this was a made-up story, then this is the only story Jesus made up, and he told it as if it were true. Essentially, those people are hoping that this is made up because they do not want there to be any realm of torment after death. That is very unlikely. Jesus did not have to tell a lie to teach people the truth. He is the truth.
Since Luke 16 is true, then people are judged when they die and not when the books are opened at the final judgment as described above in Revelation 20. Actually, there is no problem whatsoever with Revelation 20 mixing with Luke 16. Even in our court systems on earth, there are three parts to a judgment. There is the judgment when the defendant is found guilty; the second judgment when the sentence is pronounced; and the third judgment when the sentence is executed. So, in the case of a heinous crime, the prisoner may be found guilty one month and it may be several months later before he finds out how long he will spend in prison or if he possibly gets the death penalty. However, he starts spending time in prison long before he finds out how long he will have to be there. For something like the death penalty, he then sits for a long time (at least here in the U.S.) before all the appeals run out and the execution is carried out. This all matches what is in Luke 16 and Revelation 20. At death, the soul goes to where it belongs. Revelation 20 says that what occurs on the last day is that the books are opened and man is judged based on what was written. If his name was written in the book of life, then the judgment on the guilt or innocence of a person has already been made and recorded. The only thing that is new here is that it will be revealed and the final punishment imposed. Righteous people go to a place of rest described variously as Abraham's bosom and paradise. The unrighteous go to torment. It is not a pretty picture. As Hebrews 10:31 says, "It is a dreadful thing to fall into the hands of the living God."