Yes.
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.
Yes, but he cannot use his/her hands.
The goal keeper handling the ball outside of the penalty area is the same as any player deliberately handling the ball; a direct free kick. In the circumstance you describe the referee will see such minor violations as trifling and will warn the goal keeper to watch his line more carefully. Only flagrant or very frequent incidences will cause a direct free kick to be awarded. Often the keeper actually lets go of the ball in the area and makes foot contact with it outside the area.
No, the keeper cannot pick the ball up after his own player intentionally plays it to him using the feet.
A goal keeper is allowed to touch the ball with their hands when the ball is inside their own penalty area. If a goal keeper does so outside of the area, then a direct free kick is awarded to the opposing team.
If by goal box you mean goal area, a box 6 yards from the goal. Then Yes, a goal may be scored within the box. EXCEPT: A goal cannot be scored on yourself from a goal kick or free kick awarded with in the your own goal area. If the ball is kicked from a goal kick or free kick awared with in your own goal area and enters your own goal the proper restart is a goal kick as the ball must leave the pentaly area to be in play. FIFA Laws of the Game.
Yes, you can kick the ball to your goalie/goal keeper. However, if you kick your ball into your net, your team will be very mad at you because you will have given the other team a point. If you are kicking to goalie, make sure the goalie can catch the ball in order to kick or throw it far away from your goal.
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.
A goal keeper may release the ball back into play in any way they wish.
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 the ball is on the opposing team's half of the field, the keeper would then perform a goal kick.