How can I change the biome? I select the biome, click LMB and nothing happens!
Biomes are changed using RMB in brush mode (i.e. if you hold down RMB, the biome will change for all tiles that your cursor falls on)

Temperature, rainfall or other tile parameters do not change
See the answer above

Mountain type does not change
The type of mountains is also changed by pressing RMB. Also, the modified biome will overlap the image of the mountains until you update all the layers ("Regenerate all layers")

What does it mean to update all layers/specific layer?
Layers render objects and the game cannot render new (or changed) objects dynamically. This requires regenerating the layer. On large maps (100%) this can take a long time (in a sense, regenerating all layers is rebuilding the map).

I changed the biome, but nothing has changed visually
Sometimes it happens. Restart the game or use layer regeneration

Can't change the type of stones
!!! After changing the list of stones, you need to right-click on the tile again !!!

but if that doesn't work...
Thanks @Overquoted: It's a mod conflict with KV's Configurable Maps. Disabling that mod allowed me to edit stone types where I previously was not able. Load order was irrelevant. Tested using Core > Hugslib > World Edit > Configurable Maps.
The other mod conflict I found was minor and could be corrected in the other mod's settings. I mentioned it in your Bugs thread (Prepare Landing, for anyone curious).




TODO
- Replace biome to another biome