Nice post! Some comments:

In 1964, six physicists including Peter Higgs published a paper which proposed a solution to this problem and predicted the existence of a new quantum field, now known as the Higgs field.

Strictly speaking, there are three papers, and we should talk about the Brout-Englert-Higgs mechanism to be precise (as you are Belgian, you may appreciate it ;) ). However, we talk also about the Higgs boson as this has been proposed by Higgs alone.

And so while it is theoretically possible to generate a Higgs boson from the collision of an electron and a positron (which is not too difficult), in reality the probability of doing so is extremely low because electrons are very light.

Actually, it is possible and this is one o the main motivation of some of the potential future collider experiments. The idea is not to produce a Higgs boson directly from an electron-positron annihilation, but to produce an virtual Z-boson that will radiate a Higgs (we call that Higgsstrahlung). This was also the key process to Higgs searches in the good old LEP experiments.

However the Higgs Boson has a good probability to decay into a pair of top quark and anti top quark, which will themselves decay into photons.

This is incorrect. The Higgs boson cannot decay into two top quarks (the Higgs mass being smaller than the top mass) and top quarks decay almost in 100% of the time into a W-boson + bottom quark system.

Today the Higgs boson has been observed through many of his main decay modes. The diphoton one is rare, but clean. Which is why it was one of the preferred mode.