Answer:
I have a name that's not mine and no one cares about me in their prime. People cry at my sight and lie by me all day and night.
I am drawn by everyone without pen or pencil
I have a little pool with two layers of wall around it. One white and soft and the other dark and hard. Amidst a light brown grassy lawn with an outline of a green grass.
Turns me on my backs and open up my stomach. You will be the wisest of men though at start a lummox.
I let water fall on you while everyone else stays dry.
My first is snapping, snarling, growling, My second's industrious, romping, and prowling. Higgledy piggledy Here we lie, picked and plucked, and put in a pie.