Not sure how/if you can make an object enter a scene at a specified frame, though you can key-frame which layer an object is on. Essentially, making it visible at an arbitrary frame.
Shape keys will let you change a cube into a sphere or vise-versa.
Leaves on a tree? I’d just make a poly plane, divide it down the middle, then divide it 4 or 5 times along it’s length. Adjust the verts to give the shape you need, extrude it for thickness, then either manually, or with the aid of a lattice, bend it into shape lengthways and width-ways. Neal Hirsig has a good video tute on using a lattice to bend stuff.