Is the prayer invalid if the Imam forgets the first tashahhud and the congregants alert him, so he sits for the tashahhud? And what are the implications for the Imam in this situation?

If you return to the middle tashahhud due to ignorance or forgetfulness, your prayer is valid. However, if you had already stood up straight and begun reciting, and then you returned knowingly and intentionally, your prayer is invalid. The same applies, according to some scholars, if you returned before beginning the recitation. Since you have repeated the prayer, there is nothing upon you, no sin, and no expiation is required.