Platelets, also called thrombocytes (thromb- + -cyte, blood clot cell), are a component of blood whose function (along with the coagulation factors) is to stop bleeding by clumping and clotting blood vessel injuries.
Milk of the poppy is essentially the Westeros version of morphine. Maesters make it from crushed poppy flowers, and morphine and other opiate-based drugs are made from poppy plants. Indeed, the books' descriptions strongly suggest that the poppy is intended to be the real-world opium poppy (Papaver somniferum).
Global production of poppy straw containing morphine as the main alkaloid has fluctuated between 30,000 and 52,000 tons per annum. Morphine is extracted from opium resin or poppy straw in a series of extraction and purification steps involving water, organic solvents, and pH adjustment.