oggers, in your columns example, surely all 'columns' of air have to be the same height, as they all go to the same height in the atmosphere?
They do not go to the same height because they represent columns of different density. The concept is validated by the real world observation that the tropopause is much lower over the poles than it is over the equator.
I understand your desire to learn each process in detail but sometimes like a jigsaw puzzle the individual pieces in the box make more sense as you assemble the big picture.
Now back to the detail
If the plane flies at a consistent true altitude from 10c to 5c I thought the cold air will be more dense (because cold air is denser than hot air - Charles’s Law
It depends. The airmass it flew into may be cooler but that does not mean the cooler air at the same true altitude is more dense. If both columns are at the same surface pressure the cooler column will be more dense at the surface. But the pressure will fall more rapidly in the cooler column. At some given height the density of the cooler column is less than the warmer column. That is a key concept to understand.