Yes so long as he did not receive the ball from one of his own team mates.
No. Only in the penalty area may the goal keeper handle the ball.
Yes, cannot hand ball a back pass or outside the penalty area.
As long as the ball is inside their penalty area a goal keeper may handle the ball. The position of the ball is important. The position of the goal keeper is not.
In short, no. A goal kick is not complete (the ball in not yet in play) until the whole of the ball crosses the whole of the penalty area line and into the field of play. If the goalkeeper touches the ball before it completely leaves the penalty area, the goal kick must be retaken. If the goalkeeper touches the ball with his hands after the ball has left the penalty area and become "in-play", then he is guilty of a handling infraction because the ball is not within the keeper's own penalty area anymore. Either the ball is still in the penalty area or it isn't; it can't be both. This is all without even considering the fact that a goalkeeper cannot handle a ball that has been intentionally kicked to him by a teammate, the so-called "pass-back" rule.
Yes. A goalkeeper can dribble the ball back into the penalty area and pick it up. However, this is not the case if the ball was passed to him by a teammate (back pass), or if he has (for example) thrown the ball outside of the penalty area only to dribble it back in (double touch), or in any other case specifically disallowed by the laws.
I'm going to assume that you are asking about a ball that is deliberately kicked back to the goalkeeper by a teammate, then picked up. If the keeper touches the ball with his hands outside of the penalty area (the "18"), the offense is handling and the other team is awarded a direct kick from the spot where the keeper first touched the ball with his hands. If the keeper touches the ball with his hands inside the penalty area but outside the goal area (the "6"), the offense is goalkeeper handling and the other team is awarded an indirect kick from the spot where the keeper first touched the ball with his hands. If the keeper touches the ball with his hands inside the goal area, the other team is awarded an indirect free kick from the spot on the goal area line nearest where the ball was first touched by the keeper.
No. It doesn't matter where the goalkeeper is.The ballmust be in the penalty area (on the line is inside) for the keeper to touch it.
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.
A goal keeper may never use their hands outside of their own penalty area. A goal keeper may not use their hands, even in their penalty area, when a team-mate deliberately plays the ball to them with their feet. A goal keeper may not use their hands, even in their penalty area, when a team-mate directly throws the ball to them on a throw-in.
Yes. The goalkeeper may leave the penalty area at any time during play, but cannot touch the ball with his hands while outside of the area.
With two exceptions, a goal keeper may deliberately handle the ball within their own penalty area.
The goal keeper may touch the ball with his hands and arms in his team's penalty area.