Yes. It may come from a practice routine, but it is still open play. The taker has touched it, there are no restrictions on the defending team. Play is open to everyone.
Same thing.
A corner kick is a method of restarting play.
A corner kick is awarded when the whole of the ball passes over the goal
line, either on the ground or in the air, having last touched a player of the
defending team, and a goal is not scored in accordance with Law 10.
A goal may be...
Open play means the ball is in play.
From the laws of the game:
Free kick inside the penalty area
Direct or indirect free kick to the defending team:
• all opponents must be at least 9.15 m (10 yds) from the ball
• all opponents must remain outside the penalty area until the ball is in play
•...