Is the aforementioned Hadith regarding Allah's acceptance of a single prostration and the nullification of deeds due to showing off authentic, and what is the ruling concerning someone who forgets to say the glorification (tasbih) in rukoo' or sujood while being a follower (ma'moom) in congregational prayer?

This statement about the Prophet, may Allah bless him and grant him peace, has not been found with a sound or weak chain of transmission in the accredited books of Hadith. Ibn al-Jawzi mentioned it in his book "Bustan al-Wa'izin wa Riyad al-Sami'in" (The Garden of Preachers and the Meadow of Listeners), but this book contains many weak and fabricated Hadith. As for the second question, the Imam carries the prostration of forgetfulness on behalf of the congregant (Ma'mum). So, whoever forgets an obligation of prayer, such as saying "Subhan Allah" in bowing or prostrating, while being a congregant, owes nothing.