Why Are Propeller Blades Twisted?

There is a twist along the length of a propeller blade because the blade speed is much higher at the tip than it is at the root. The twist is necessary to maintain a more or less constant angle of attack along the length of the blade.

Why does the blade angle of a propeller change from root to tip?

During one full rotation, the tip of the blade has to travel a much further distance than the blade root, all in the same amount of time. That's why the blade angle is greatest at the root, and the least at the tip. By "twisting" the blade, you get a relatively uniform angle of attack across the entire propeller blade.

Why does the shape and angle of a propeller blade change from the hub to the tip?

The reason for placing the blade element sections at different angles is because the various sections of the blade travel at different speeds. The inner part of the blade section travels slower than the outer part near the tip of the blade.