I'd go with witch hazel for the left leaf. Their seeds mature in early fall and get forcefully ejected, sometimes falling 20 feet or more from mama. Witch hazel is a woody shrub that rarely gets over 20' tall. And you're correct about beech - their nuts grow in a spiky 3-panel package about 1/2" diameter, with a single triangular nut within a hard-to-remove hull. Quite tasty straight from the hull, though one might starve to death trying to free them from their covering. Kind of like celery - chewing that veggie takes more calories than it provides.
Of course, if one eats beechnuts like a bear, spiky covering, hulls and all (and as fast as they can get crammed into the bear's mouth) the energy budget is more favorable. At least in Maine, bear reproduction is keyed to beechnut crops; lots in the fall, many cubs in the spring.