can the coach take out the pitcher put her on first base or any where on the field then later put her back to pitch?

This is legal as long as you keep her in the game. In some leagues, once you have taken a player out of the game and put her on the bench, she is ineligable to play the rest of the game.

depends on your league's rules. obviously in real baseball you can't but some leagues could be soft on rules since its little kids. But on the other hand it sounds like the coach is changing her position because he's worrying about winning and not about every player being able to play.

Yes, if the player has the skills on other bases, also infield or outfield, why not? And if the coach has another good pitcher in team, he can interchange his players as long as they have the potential in doing such rule.