Why does putting a heavy book on a crumbled piece of paper make it flatten out, and why does it take 10-15 minutes for it to happen, not instantaneously?

Okay, the answer to this can be rather complex.

First, don’t think of the paper as a single object but rather as a net (really more like threads placed in random directions) of single thread-like fibers. When you crumpled the paper you bent each of the threads along each crease beyond their ability to bend (think of metal bars that are now bent). Each of the fibers is either broken, cracked or deformed (narrowed along the length of the bend).

Now you flatten it out. The broken and deformed pieces no longer fit the same way as the original flat paper as they no longer have the same shape. Now these fibers are pressed against each other (from the book) and must drag themselves across each other until they reach a point of equilibrium between the pressing of the book, the friction of the other fibers and elasticity of the fiber itself (the tendency of the fiber to assume its neutral shape).

Just like things at our scale need time to move and shift, this is also required at the scale of the fibers as well.

If you want a slightly more mathematical answer we can go with Newton’s Second Law (F=ma). If you apply a force to any given mass, a time component is needed as part of the movement. This continues until all forces come into equilibrium.