"You seem to have decided to ignore, without any justification (if there are some, please show them), hundreds of year of data (experimental measurements, i.e. facts), the underlying theory predicting them (that has not been falsified so far),"
-Consider for one moment that maybe the data is wrong. Perhaps you where even lied to. To not consider this would be, by definition, naive and gullible.
If I predict something ridiculous (such as a thing that has no dimensions or takes no space)and you could not prove me wrong, would that make me correct?.
"and numerous applications in our every day life (including current communication means, computers, etc.)."
-Computers take up space so I don't see how they have anything to do with point particles.
"PS: mass is different from weight (mass is constant, weight can change), and things can exist without taking space (for instance: light)."
-And I would like to see an example where you can add to the mass without weight changing. Weight is just a measurement of mass. In the way that distance is a measurement of the volume. and quantity is the measure of density.
Where is the thing (for instance: light) if it takes up no space?? Seriously where is it????? If it takes up space you could define its position (the space where it presides). If it is not some where it is NO WHERE.
To find the Mass of a black hole or a point particle you must divide the density (1 sun for example, or one particle) by the volume (no pace is zero volume). You can not divide anything into Zero. If you do not believe me get your calculator and divide any number by zero.
Personally I have never seen anything that came from nothing. And if it takes up no space it obviously is not here.
Try to imagine a "thing" that is "no where". This is the theory of point particles and black holes. No one has or can witness ever witness these fictional, impossible entities.
I am not trying to attack your science, friend. It would not be science if we did not question it.
Tell me friend. Do you believe in the Big Bang "theory" where the universe was born from nothing in an explosion??