Correct me if I'm wrong, but I believe red poppies grew in abundance in the fields of flanders soon after WW1 ended. Something to do with the severe disturbance of the soil and whatnot. Poppies were the first plants to recolonise the area around the trenches. I think that's why poppies are used to remember the dead.
Yes, that's correct. Major John McCrae wrote the poem
In Flanders Fields in May 1915 in Ypres. It related the dead soldiers there to the poppies growing there, and the poppy has become the symbol of remembrance of dead soldiers based on that poem.
