As you can imagine, I have a few comments about a few imprecisions. Please consider correcting the post ;)

Everything must have been a single point – a singularity.

Strictly speaking, we do not know what happened at the origin since there is no such a thing. This is the limit of the time going towards zero of the theory, and the theory is ill-defined on that time. Moreover, there was no spacetime at that moment, and thus no time in particular. So stating that the origin is a ‘single point’ is not really correct, and a ‘singularity’ is incorrect (this only means that the theory diverges). But you got the rough image right.

here are also missing observations: no one has detected gravitational waves, let alone gravitons, the particles that theory predicts carry the gravitational force.

Gravitational waves have been detected! There was even a Nobel prize for that 2 years ago!

There is also the puzzle that most of the mass that must be in the Universe to explain gravitational effects seems to be undetectable.

This is only partly true. Dark matter can be detected, at least indirectly (the cosmic microwave background, gamma rays, galaxy formation, etc.). Please see here (damned I wrote this 3 years ago ;) ).

Expansion continues, and the tightly packed highly energetic photons convert some of their energy into a sea of virtual quarks which combine to form larger virtual particles and antiparticles. Virtual particles of matter exist for only a very short time. This is allowed by the Heisenberg uncertainty principle, provided that their mass-energy and lifetimes multiply to a smaller value than the Planck constant h.

A virtual particle is virtual and therefore not real. This is just a quantum field theory calculation artefact to explain some effects.

The large uncertain quantity here is H, the Hubble constant

H is pretty well measured today, at the 1% level.

The density of the Universe is not easy to measure. One way is to add up all the matter we can see in stars and galaxies, make some corrections for the clouds of invisible hydrogen gas and other small particles and hope for the best.

Not really… As there is a lot of invisible stuff. The easiest is to extract it by fitting the cosmological model altogether.

There are three possible fates for the universe.

You may want to say that according to the above mentioned fit, the universe is flat.

There could also be black holes, just small enough (which has been confirmed already).

Really? Not to my knowledge. Black holes dark matter is just one hypothesis amongst many others.