Yes they can. This is considered a delay or game and it is usually every 10 seconds. He can also calls balls if the pitcher takes more than 10 seconds to start her pitch after contacting the rubber.
Baseball is an odd sport in that the defensive team has the only opportunity to score points. The pitcher has the single most important offensive position in the game. If the pitcher does not succeed in his goal of getting the ball past the batter, then the other members of the offense must "take up the slack." However, the defensive batter has the only position that can score. If you are in the dugout, then the most important player to you is the batter. If you are in the field, then the most important player is the pitcher. If you have a bat in your hand, then you better be sure the most important player is you.
The Dugout
Yes.
The batter is out any time the umpire judges that she has abandoned her attempt to run the bases. In this case, the umpire will probably judge that turning toward the dugout (especially if she advances toward the dugout) is an abandonment of her attempt to run the bases and call her out.
Yes, the ball is live, so there are several ways the batter-runner could be called out after a walk. One would be if he goes from the batter's box into the dugout; another would be if he goes to 1st base, then rounds it and is tagged. I'm sure there are more.
When a fly ball is caught, the batter doesn't do anything but go back to the dugout.
because one of his teammates will bring it to him.
Anytime a manager advances from the dugout and says something to the pitcher it is considered a visit to the mound, unless it is in regards to an injury, in which they can only discuss the injury. If a manager visits the mound and then turns back to the dugout and then turns again to say something else, this is considered a 2nd visit, and the pitcher will by rule have to leave the game. Generally you will see catchers look into the dugout and the manager will give him a sign to go out and talk to the pitcher
sometimes the manager gives the catcher signs from the dugout. the catcher gives the sign to the pitcher what he recommends if he doesn't get a sign from the dugout. in the end, obviously, the pitcher has the final descision on what he wants to throw, but as the level of play increases, pitch calling becomes more dependent on the catcher.
No
It is called a foul
in the game of baseball is the batter turned runner automatically out for going into the dugout thinking the play would be made, but the first baseman was never on the bag when the throw was received?