Generally if you remove a threaded pipe, it goes back in with either pipe dope or tape.
For the shower arm, it's easier to turn them with the head on the arm, even if it's not tightened all the way yet. It gives you more leverage having that on the end.
For the tub spout, you may need a new pipe nipple anyway, depending on the length you will need. But if the old one is still good, then that's okay too.