Does CO2 strengthen the mid troposphere inversion layer ?

Carbon dioxide would probably do the opposite. It warms the lower atmosphere and cools the upper atmosphere.

I may not be a scientist but I can recognise "interesting" science when I see it.

What basis do you have for saying that the CO2 molecules will be drawn to earth because of the negatively charged oxygen atoms? Won'CO2 be repelled because of the positively charged carbon atoms. Or is it just electrically neutral so won't actually be attracted anywhere.

If you had said CO2 would fall down because it is heavy then you might have a point. Except that if that were true we would be "living" in a layer of CO2 - which means we would not be living at all because we can't breathe CO2.

I was not sure what he freezing point of CO2 had to do with anything either.

However, I do suspect that greenhouse gas distribution does affect the climate.

What "mid troposphere inversion layer" are you talking about?

Trade wind inversion?

Subtropical anticyclone inversion?

Frontal inversion?

By the way, your "Additional Details" make little sense. Carbon dioxide is an uncharged, nonpolar molecule--it does not get drawn back to the surface.

It is fairly well-mixed in the troposphere, why wouldn't it be? Convection does a fine job of mixing it. Its molar concentration is less in the stratosphere, but not that much less.

EDIT: That's not a particular inversion--it could be any of those that I mentioned. There could also be no inversion at all--certainly many regions of the world have no inversion in the mid troposphere. The inversion strength is determined primarily by meteorological conditions, not by CO2.