In the "double-slit experiment" - did they actually shoot individual particles/electrons? When describing the experiment - it is usually described that first, a wave was shot through two slits, than "individual particles" was shot through the slits (and then an interference pattern surprisingly appeared on the screen) - but is it really possible to shoot "individual particles"? What does it mean? How did they do it?
And, this experiment shows that light is actually a wave, and not particles - what part of the experiment (or another experiment) actually shows that light is "also made of particles"?
 A: You have to go back a few hundred years for the history of this experimental setup. The Double Slit experiment was performed by Thomas Young  in  1801 to show that contrary to Newton's idea about light being composed of particles, light was actually a wave. The diffraction aspect was what interested Young, because waves are the only phenomenon that can undergo diffraction.
Later, more sophisticated experimental methods were developed that allowed less and less photons through at a time, until we get to today with single  electrons and 800 atom  molecules, all of which undergo diffraction.
As far as single photons are concerned, I would give you three different versions of what this means:


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*Single Photon Experiments from this site, and the comments on that page regarding the use of single photons. 

*Double Slit Experiment  from Scientific American

*Single Photon Sources From Wikipedia

Please also see this answer by anna v, Single Photon Double Slit Experiment, which contains images of the twin slit experiments.

But, like lots of ideas in physics, although the results of the experiments did not change, the interpretation of what they represent underwent a few changes up to QED's presently widely accepted picture.
The link on below tells you more about the actual details of how you get to the one photon level.
Single Photon Production
To demonstrate that photons can viewed in particle terms, please read Photoelectric Effect, which shows that if light was made of waves, we would be waiting a long time to accumulate enough energy to free an electron from a  metal surface.
So today we deal with fields, rather than worry (so much, anyway) about wave / particle "duality".
