no

No. If you could do that, it would permit things like a virtual "designated hitter" in the National League, where you substitute for the pitcher every time he comes up to bat.

You cannot remove ANY player in MLB, have them sit out part of the game and then return. You can have them change positions in the field and then return to their original position however. If you do this with your starting pitcher and he qualifies for the win, he cannot also get credit for a save.

Actually, you can... so long as you don't take him out of the lineup and so long as you don't bring him back in during that inning in which you remove him from the mound. A few years ago, the NYMets ran out of pitchers in a game and needed, desperately, to bring in a lefty (Jesse Orosco) against a big lefty on the other team. I believe Roger McDowell was on the mound at the time and, if the Mets pulled him, they would have no other right handed pitchers. So, Bobby Valentine (the manager) pulled his right fielder and moved McDowell to right bringing Orosco into the game. The next inning, McDowell returned to the mound (I don't recall if Orosco swapped out to right or if Bobby V brought in a regular fielder, but that does show that you can take a player off the mound then return him to the mound later (so long as you don't take him out of the game). As an aside, should a pitcher be able to throw with either hand, the hand with which he steps on the mound once a batter is in the box is the hand he must use for the duration of that at bat. If the batter is a switch hitter, he has the option, always, of turning around to face the pitcher at his more advantageous side. Still, the pitcher SHOULD already know from which side the hitter is best at and can establish the match-up. No charge.