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).
I got some poppy starts from a very old lady in Oregon. They were tall and beautiful pink poppy's. I had them for years and didn't know they were opium poppies until I saw a documentary on Discovery about growing opium and went out and looked at mine and sure enough that's what they were.