PQ and soil improvement

Agreed; purchasing a "Soil Improvement" tech with the "BUY" button does not turn the tile green; instead it places a "soil improvement" structure on the tile, which just sits there doing nothing. The Soil Improvement structure is somehow complete (because it was purchased, rather than built) but at the same time it fails to turn the tile green and go away.

PQ numbers seem to list the maximum tiles a planet can hold, which includes yellow tiles (and maybe red tiles if such a thing exists?). It can be argued that planet quality should track the planet's current green-tile count. That problem is a question of the definition of Planet Quality.

Can the player improve a planet's quality by the use of Soil Improvement and other such technologies? It seems that it would be splitting hairs in a rather confusing manner to decide that this is not a change in planet quality. Changes in PQ rating would also become a reward mechanism for the player, and worth considering.

PQ numbers seem to list the maximum tiles a planet can hold, which includes yellow tiles

No, it is the number of green tiles at the start of the game.

Right you are; I didn't take into account the colonizer tile. As you said,

it is the number of green tiles at the start of the game.

I've noticed that sometimes, the tool tip showing a world's Class doesn't match the world's listed class. I presume that the tool tip is showing the "fully formed" number, as it is always equal to or greater then the world's listed class.

I have also noticed that there is only one 'formable tile on worlds that have yellow tiles. I wonder when multiple yellow tiles will make their first appearance?

I wonder when multiple yellow tiles will make their first appearance?

I have already seen multiple yellow tiles. I don't have any feel for what the basis is for generating them, even after reading the GC2 journals, but so far it looks random, with perhaps a minimum starting PQ to get even one.