Yes. The ball is moving, right? It has both momentum (mass times velocity) and kinetic energy (one-half the mass times the velocity squared). When you hit the ball with the bat, the energy of the ball is transferred to the bat, and the bat imposes its own energy and momentum to the ball.
friction
When the ball hits the bat then the ball feels as much force as the bat does hitting the ball
(0.143 kg) (8500 m/s2) = 1215.5 N
They don't cancel because they are acting on different objects. The bat exerts a force (hitting) on the ball, and the ball exerts a force (pushing off) on the bat. If the ball were being pushed from two opposing directions, it would not move.
Of course it does. Any matter undergoing the force of gravity can exert a force on an object.
Yes, an equal and opposite force.
zero
When a ball is being struck by a bat it certainly exerts a reaction force on the bat. But the bat does not move backward because the reaction is not enough to move the bat as it is much heavier than the ball. The reaction force is felt by the person who strikes the ball with the bat through his arm. If the ball is heavier than the ball the bat will surely get the reaction force and move back.
-50 N
Since you need to exert force on the ball to push it away from you, the ball will obviously push back (with a force that has the same magnitude, but is in the opposite direction). This is an example of Newton's Third Law.
friction
1000 N as well.
All of the fundamental types of force can be mathematically described in the form of force fields. But force involves many things. If I throw a ball, I exert force on that ball which is then accelerated as a result. The force field involved is far from obvious, although it does exist. If you understand the physics deeply, you would see that in order for me to exert a force on a ball, the electrons in the atoms in my hand have to exert a force of repulsion on the electrons in the atoms of the ball. And that electromagnetic force can be described as a force field.
gravity
When the ball hits the bat then the ball feels as much force as the bat does hitting the ball
Speed of bat x weight of bat is force applied against ball's speed times ball's weight.
Force is a concept and is invisible. An example will be that you use to pull apart two magnets that are stuck together. That effort to pull the two magnets apart is a force. When your airplane is taking off, you feel your back is being pushed against your seat. What you are feeling is the force that the seat cushion is applying on you. When you hang a weight on a spring, the spring elongates. A force is applied by the weight on the spring to cause the lengthening of the spring. When you hit a softball, the softball flies away because you exert a force on the bat; the bat hits the ball; the ball stores the kinetic energy and then releases the energy as a force pushing on the ball until the ball leaves the bat.