If the goalkeeper tries to release the ball using a bad drop-kick, but misses the kick and the ball lands outside the penalty area, can they run up and kick it?
There's nothing in the rule book that forbids it: law 12 -- fouls and misconduct -- Indirect Free Kick.
Fouls commited by the goalkeeper are:
- When the ball has been deliberately kicked back to them by another player on their team.
- When they receive the ball directly from a throw-in by another player on their team.
- When they have held the ball continuously for 6 seconds.
- When they have already held the ball for 6 seconds and released it and it has not been touched by another player.
These situations are where he can't use his hands. But he can release the ball (him being inside the box, ball thrown outside the box), then control it with his feet, and kick it.
If you put a ball back into play by dropping or rolling the ball on the ground in front of you, it's considered distributing the ball. Then you can't pick it up again using your hands (even thought you are within your own 18 yard box). What you did was to set the ball in play by putting it on the ground and then you can kick it away from you.
I can't see a situation where a failed attempt at dropping/kicking the ball would be seen as a foul/misconduct, and the referee to blow the whistle. A step-by-step action would be: 1. I handle the ball 2. I release the ball 3. I kick the ball with my foot. At no stage there's handling back the ball (that would be a foul).