If the ball was thrown-in by a teammate, no.
If the ball was thrown-in by an opponent, yes.
No he can't, because that will consider as a pass.
No, the keeper cannot pick the ball up after his own player intentionally plays it to him using the feet.
No.
Yes. If the ball is kicked to them or thrown-in to them directly from a team-mate. If the goal keeper releases the ball from their hands they cannot pick it back up again until another player touches it.
yes
If it was thrown-in by an opponent, then play continues. If it was thrown-in by a team-mate, then the restart is an indirect free kick for the opposing team.
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.
If a defender passes the ball back to his own goalkeeper using his feet then the keeper cannot pick it up, he can only use his feet to clear or pass the ball. however if the defender passes the ball back to his keeper using another part of his body (excluding arms and hands) then the goalkeeper can pick it up.
A goal keeper may not touch with his hands a ball directly thrown-in to them by a team-mate. If they do, then an indirect free kick is awarded at the location it was touched.
A goal keeper may not handle the ball if it is passed to them from the feet of a team-mate. If they do, an indirect free kick is awarded to the opponents at the location of the handling.
You are absolutely correct. If, in the opinion of the referee, a player kicks a ball up into the air to deliberately chest or head the ball back to his own keeper to permit the keeper to "fairly" play it with the hands, it is a violation of the Laws of the Game and will result in a caution for Unsporting Behavior. The maneuver was done to circumvent the rule regarding the backpass to the keeper.Oh, and the keeper can pick up the ball in the above situation, but it will result in a whistle and the awarding of an indirect free kick to the other team at the spot where the keeper touched the ball. But you knew that. Good for you!
Yes so long as he did not receive the ball from one of his own team mates.