The goalkeeper has caught the ball and decides to put it on the ground to kick it to his teammates.
Is the ball considered to be in play? Can any other player, including the opponents, play it from the ground and score?
Yes, the ball is in play - but it was in play before the goalkeeper put it on the ground as well. Quoting Law 9, The Ball In and Out of Play:
1. Ball out of play
The ball is out of play when:
- it has wholly passed over the goal line or touchline on the ground or in the air
- play has been stopped by the referee
2. Ball in play
The ball is in play at all other times, including when it rebounds off a match official, goalpost, crossbar or corner flagpost and remains in the field of play.
As long as he just caught it, so it is no goal kick, free kick or something similar, the ball is in play when he stops controlling it with his hands. So if he puts it down, the ball is in play, the moment his hands leave the ball.
As can be seen in rule 12-2 (Indirect free kick):
An indirect free kick is awarded if a player:
- prevents the goalkeeper from releasing the ball from the hands or kicks or attempts to kick the ball when the goalkeeper is in the process of releasing it
A goalkeeper is considered to be in control of the ball when:
- the ball is between the hands or between the hand and any surface (e.g. ground, own body) or by touching it with any part of the hands or arms except if the ball rebounds accidentally from the goalkeeper or the goalkeeper has made a save
- holding the ball in the outstretched open hand
- bouncing it on the ground or throwing it in the air
A goalkeeper cannot be challenged by an opponent when in control of the ball with the hands.
The rules do not include any other things why he is still controlling it.