Does the prayer of one who adds "peace be upon the Prophet, may Allah bless him and grant him peace" in the first Tashahhud, then remains silent, become nullified, whether she is praying in congregation behind the Imam or individually?

The prayer is not invalidated by invoking blessings upon the Prophet, whether done intentionally, out of ignorance, or forgetfulness, and whether the worshipper is an Imam, a follower, or praying alone. This is because it falls under the category of extra verbal utterances in prayer that do not invalidate it even if done intentionally, similar to reciting Quran during bowing or prostration. The Sunnah (definition) is to confine oneself to the Tashahhud (definition) only in the first Tashahhud, without invoking blessings upon the Prophet or making supplications, but there is no harm in performing them.