Hi Bernard,
Welcome to the club!
Answering your questions:
1. Everyone is allowed to be everywhere they want on the playing
court, including the GK area.
2. A goal may be scored from anywhere on the playing court, including
either GK area.
3. The "goal kick" is called Goal Clearance, and it must be taken by
the goalkeeper with his hands (not feet).
As in soccer, the goalkeeper cannot receive a pass back from his
teammate and pick up the ball with his/her hands. Also, in Futsal, a
goalkeeper can only receive a pass back from his teammate with his
feet (no hands, ever) when 1 of 2 things happen (write it down
because most of the USFF referees don't get this):
a) the ball must touch an opponent
b) the ball must "clear" to the opponent's half of the court.

Any other questions, please feel free to contact us.

Robert Magellan