Does a slight tilt backward and then forward before prostrating, and remembering the saying "My Lord forgive me" and uttering it, then descending to prostrate, affect the validity of the prayer, and is that considered an intentional addition of a pillar?

The action of the person mentioned, represented by leaning backward, does not invalidate his prayer, because it is a slight movement and not from the same type as prayer, and it does not necessitate a prostration of forgetfulness (sujood as-sahw). Excessive movements are of two types: additions that are of the same type as prayer, which invalidate the prayer if done intentionally and require a prostration of forgetfulness, and additions that are not of the same type as prayer, which invalidate the prayer if many, but are excused if slight, and do not require a prostration of forgetfulness.