Sand to Grass:
The best way to convert a desert (sand that does not border water) tile into grass is to increase the humidity to over 100% and have the fertility at or above ~30%. This will convert the tile to grass, but it tends to not be stable at first. The best solution is to make a group of grass tiles bordering each other. This will make the grass stable.
Grass to Forest:
Forests cannot border sand. Grass with high enough flora will convert into forest.
Forest to Rainforest:
Forests in the correct temperature and surrounded on all sides by forest will convert into rainforest.
There should be some sort of endless mode in the challenges where there is no enemy queen, but enemies just come from the right in ever increasing numbers and you have to defend yourself. It would maybe keep track of how many you killed or something like that.