Does slight movement invalidate prayer, whether for concentration, an itch, or other reasons? Is intense focus required to avoid any movement in prayer? And what should a worshiper do if the imam is fast and moves before the worshiper has attained calmness in their position?

The remedy for the whispers (waswas) you are experiencing is to ignore them and turn away from them. As for minor movements, they do not affect the validity of the prayer. Your lagging behind the Imam is not permissible if done intentionally; you must promptly move as soon as the Imam finishes reaching the rukn (pillar). If the Imam precedes you due to his speed without any negligence on your part, then there is no blame on you; perform the rukn and then follow the Imam.