The rock is 4 inches (~10 cm) long. The vendor claims this rock is from K2. Are the blue spots real or painted on?
The blue spots are natural. This rock is indeed granite from K2. The blue spots are azurite. Malachite is also reported from this same location. From Geology.com:
"K2 granite is named after a mountain in the Karakoram Range near the border between Pakistan and China. K2, also known as "Mount Godwin Austen," is the second-highest mountain in the world. The azurite granite is found in colluvium near the base of the mountain."