We're already seeing all the way back to within 380,000 years of the origin of the Universe when we detect the cosmic microwave background radiation (CMBR), created when protons and electrons were first moving slowly enough to be able to combine to form hydrogen atoms. Before that, the particles comprising the hot primordial plasma were moving so fast that they could only collide and bounce off each other. The CMBR is currently coming to us from 13.7 light years away. As time goes on, we'll continue to receive it from ever increasing distances, but we'll never see it from earlier times.

There is a distance beyond which the expansion rate of the Universe relative to us exceeds the speed of light. That does not mean that anything beyond that distance is actually moving faster than light. It means only that the distances between objects at that distance and us are increasing faster than the speed of light because of expansion of the Universe. The special theory of relativity does not prohibit that.

The above perspective should answer most of the questions raised in this thread. A few questions remain.

Supernovas offer no clues to the density of the Universe at various epochs in the history of the Universe because the frequency of their occurrence in given volumes of space at various times is not known with useful precision.

Acceleration of the expansion of the Universe adds only a secondary perturbation to the history of the expansion. This evidently will not remain true in the future.