Is the prayer of the congregant dependent on the prayer of the imam, such that it is valid by virtue of his (the imam's) prayer, unless the imam commits an error? And does this mean that the nullifiers of prayer differ in congregational prayer from those in individual prayer?

The meaning of the Prophet's (peace be upon him) saying: "The Imam is a guarantor" is that the Imam is a guardian and preserver of the congregants' prayer from invalidation. He bears on their behalf some of the pillars and Sunan, such as audible recitation and the recitation of a short Surah (definition), and the forgetfulness of the congregant, and even the Fatihah for one who joins late. He also takes responsibility for supplicating for the congregants in Qunut and for teaching them the rulings of prayer. This guarantee does not mean that the congregants' prayer becomes valid if the Imam's prayer is invalid, or vice versa. Thus, invalidating violations of prayer committed by the congregant are not borne by the Imam. As for non-invalidating violations, they are rectified by the Imam's prayer.