You should use conservation of momentum. This is always conserved.

Regarding kinetic energy: It is conservation of energy, not conservation of kinetic energy. In an inelastic collision the kinetic energy is transformed into a different kind of energy

I don't know. The only example I know is that helium and H2 are that lightweight that they can escape into space. Hence the molecular weight seems to play a role, but that's all I know.

In a very simple and handwaving picture: molecules can vibrate and rotate upon absorption of electromagnetic radiation. But these are quantized energy levels. The absorption spectrum, hence the number of possible absorption lines depend on the molecule.

For example O2 has two atoms. They can vibrate against each other resulting in one set of spectral absorption lines.

CO2 has already three Atoms. Hence you get vibrational modes for first C versus the O atom, for second C versus O atom and for C versus C atom. This gives you several sets of spectral absorption lines.

As well you get different numbers of rotational absorption lines depending on the demension of the molecule. Helium is 0D, O2 and CO2 are 1D, H2O is already 2D because the angle between the bonds is not 180 degree. Methan is an example for a 3D molecule. The higher the dimension, the more modes of rotation are possible.

In general more complex molecules have more rotational and vibrational modes hence they absorb a larger number of spectral lines. Hence they absorb more infrared radiation.

For more details and a more physical mathematical description have a look at infrared spectroscopy.

> so annoyingly we don't have a benchmark for pre-pandemic rates of mental health

If you don't have data supporting your story, just don't tell your story - especially not in the headline.

It is a serious topic, and I bet better data, covering a much longer timescale, exist. Your data does not even cover two years.