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).
Because poppy seeds contain small amounts of opium, eating food with poppy seeds can cause donors to test positive for opiates. MROs are aware of this, and are trained to report the test as positive only if there is also physical evidence of drug abuse. Back to general drug and alcohol testing information.