Is the Imam correct in saying that greeting those praying during the establishment of the prayer is not from the Sunnah, and is it permissible for the Imam to come from behind the worshippers to his prayer place and for the prayer to be established immediately?

It is prescribed for both the Imam and the congregant to offer greetings of peace upon entering the mosque, due to its effect in fostering familiarity and love, and because of the generality of the hadiths narrated in this regard. This is not an innovation (bid'ah), but rather falls under the category of al-masalih al-mursalah (unrestricted public interests). Entering from any door of the mosque depends on the nature of the mosque and its entrances, and this should not be a cause for dispute or division.