Why does a diver changes his body positions before and after diving? Before a diver dives in a pool, he changes his body positions several times. When he is about to jump from board he extends his arms and legs but sometime after jumping he closes his body in a spherical shape.

Why does he do it and what effects does these changes have on speed, K.E or P.E, angular momentum etc ?
 A: 
The cited diagram depicts but a small part of the motions that occur during a dive. That appears to be an overly simplified diagram of a rather simple springboard dive, a forward 1 1/2 somersault tuck. It's overly simplified because it misses the complex motions a diver undergoes at the start of the dive.
There are two mechanisms by which a diver turns during the course of a dive:


*

*Non-zero angular momentum attained during the start of the dive, and

*Twists with zero angular momentum in the direction of the twist (falling cat physics).
Working backwards from the end to the start, the diver needs to enter the water with as little splash as possible (a noticeable splash means points are deducted). This is accomplished in a dive with N+1/2 rotations (N is an integer) by having the arms fully extended and hands together at entry into the water. The hands punch a tiny bubble-filled hole into the water. The diver's arms and body must follow this tiny hole or a splash (or worse) will result. (In a dive with an integral number of rotations, it's the diver's feet that punch a hole in the water.)
Angular momentum is more or less conserved during the course of the dive. A tuck or pike position (the diagram depicts a tuck position) reduces the diver's moment of inertia compared to the moment of inertia with arms and legs fully extended. Because angular momentum rather than angular velocity is conserved, the more compact shape of a tuck or pike position means an increased angular velocity. This increase in angular velocity is what enables a diver to perform up to 4 1/2 somersaults during the course of a dive.
That angular momentum that enables these somersaults has to come from somewhere, and that somewhere is the start of the dive. Springboard divers raise, then lower, and then raise their arms during the onset of the dive. This does two things. It makes the springboard exert a stronger force on the diver than a more passive approach (thereby increasing the diver's time aloft),  and it also imparts a significant angular momentum on the diver. Divers call this initial part of the dive the hurdle.

Even more interesting, perhaps, are the twists (as opposed to somersaults) that divers perform. The diver performs somersaults via the angular momentum attained from the springboard. Twists are different. A diver doesn't (or shouldn't) have any angular momentum normal to the somersault. Twists invoke falling cat physics. Thomas Kane, better known for developing what is now called Kane's method in robotics and related fields,wrote one of the two seminal papers on the falling cat problem (T.R. Kane and M. P. Scher (1969), "A dynamical explanation of the falling cat phenomenon," International Journal of Solids and Structures 5.7:663-IN2). The other seminal paper is by Richard Montgomery (R. Montgomery (1993), "Gauge theory of the falling cat," Fields Institute Communications 1:193-218.)
A: Before lifting off the diving board the diver legs and arms fully extended, which means that the diver has large moment of inertia $I_1$ about one axis. The moment of inertia considerable reduced to a new value $I_2$ when the legs and arms are drawn into closed tuck position. As angular momentum is conserved, the diver spins faster when its moment of inertia becomes smaller.
