To what extent is it legitimate for the Imam to step backward once when bowing (Ruku'), and another step when prostrating (Sujud), then to step forward twice to stand after rising from prostration (Sujud)? And are these steps considered an addition to the prayer?

The steps taken by the Imam for a clear benefit do not invalidate his prayer, because numerous, dispersed actions do not invalidate the prayer. This is supported by what is narrated in Sahih Muslim on the authority of Sahl ibn Sa'd (may Allah be pleased with him) that the Prophet (peace be upon him) led the people in prayer on the minbar. He said "Allahu Akbar," and the people behind him said "Allahu Akbar" while he was on the minbar. Then he raised [his head from bowing], descended backwards until he prostrated at the base of the minbar, then returned [to the minbar] until he finished his prayer. He then said: "I did this so that you may follow my example and learn my prayer."

Al-Nawawi said: This is evidence for the permissibility of taking one or two steps in prayer when there is a need, and that numerous, dispersed actions do not invalidate the prayer.