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).
In the beginning, Poppy is only a baby and is to be served to the young Prince Gristle as his first troll. However, she is replaced with a wood decoy and saved and delivered to her father King Peppy, where she is led out of Bergen Town by him to safety through his hair.