Is it necessary to say "Allahu Akbar" (God is the Greatest) for the prostration of recitation (Sajdat al-Tilawah) inside and outside of prayer, and is the Taslim (salutation of peace) necessary outside of it?

The prostration of recitation (Sujud al-Tilawah) in prayer is like the prostration of prayer (Sujud al-Salat): one says "Allahu Akbar" when going down and "Allahu Akbar" when rising up. The proof for this is the action of the Prophet (peace and blessings of Allah be upon him). As for outside of prayer, it is legislated to say "Allahu Akbar" only when prostrating, and it is not legislated to say "Allahu Akbar" when rising or to say the salutation (taslim).