Yes. A goal keeper has all the rights of a regular player, they just have a few extra rights while they are in their own penalty area.
No.
a goal keeper saves the ball and the goal shooter shoots the ball
The goal keeper defends the ball from being in the goal.
If a defender passes the ball with his feet to the goal keeper, the goal keeper may not touch the ball with their hands.
A goal keeper may release the ball back into play in any way they wish.
If the ball completely exits the field, across the goal line, between the goal posts, and under the cross bar while the ball is in play then a goal is awarded. This is true even if the goal keeper has possession of it. The goal keeper's body position would not be relevant, only the ball.
A hand touching the ball does not meet the full criteria for having possession. A goal keeper is in control of the ball: 1. while the ball is between their hands or between their hand and any surface (e.g. ground, own body) 2. while holding the ball in an outstretched open hand 3. while in the act of bouncing it on the ground or tossing it into the air
Yes
Yes.
If the ball completely crosses the goal line, between the goal posts and under the cross bar, during active play then a goal is awarded. This is true even if the goal keeper is holding or touching the ball at the time.
most of the time when a goal keeper takes the penalty shot but sometimes when the goal keeper of the other team is so much above his field or area the goal keeper may kick the ball from goal to the other goal.
No. Only in the penalty area may the goal keeper handle the ball.