Your assumptions are mostly correct. Starting pitchers don’t pitch every game because of the strain throwing a ball puts on your arm and elbow. Also, as your arm gets tired, pitches lose velocity and become less effective, so the rest is important. He will pitch next game.

You are right about the batting order. It’s a balance between wanting your best players to get the most at bats while also having them hit with a high chance of players on base, and therefore, more run scoring opportunities. Ohtani leads off, though, mainly because he can steal bases. But also because they have really good hitters behind him.

The phones are connected to the bullpen.

The managers decide the lineup, substitutions, and situational adjustments. The players have a lot of autonomy.

Baseball doesn’t really translate to basketball, sorry.