yes he/she can for example if the goalkeeper is going to kick the ball and puts it down he/she can pick it up and move it somewhere else.
Yes it can be done, as it is not a back pass.
No, a keeper may not pick the ball up on a pass back. If they do so, an indirect free kick is awarded to the opposing team.
Only inside the box.
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.
if it was not a pass back then he's allowed
yes he can. as a goalkeeper you dont give up on goal never ever!
Only if it was thrown-in by the opponents, not from a team-mate.
It depends on how the goalkeeper received it. If the goalkeeper received it from a deliberate kick or a throw-in by a team-mate, then no. Otherwise, yes.
I believe you mean the penalty area. The goal area is the smaller rectangle. If the ball was passed to the goalkeeper by a teammate with their foot then this is an indirect free kick offense. In all other cases this is allowable.
Yes, and its also one of the only cases where the goalkeeper can use his hands to pick it up from a pass from the defense.
Yes. The rule that prohibits passes to the goal keeper only specifies "kicked with the feet."