What is the optimal action that should be taken toward a mosque imam who fights against some Sunnah acts of prayer, such as placing hands on the chest and moving the finger in the Tashahhud, while also committing some Bid'ah (innovations), such as celebrating the Prophet's Birthday (Mawlid)?

Disagreement on an issue is not to be denied. Issues related to moving the finger during prayer and the placement of the hands are strong matters of scholarly disagreement, where one should not condemn those who differ. The Imam does not have the right to rule that the prayer of someone who moves their finger is invalid, nor to incite the public against them. Similarly, young people should not delude people into thinking that what they adhere to is the pure Sunnah.

An-Nawawi summarized the madhhabs (schools of thought) of scholars regarding the placement of hands in prayer: some place them under the chest, above the navel (the madhhab of the Shafi'is and the majority), and some place them under the navel (Abu Hanifa and Sufyan Ath-Thawri). Malik has two narrations: under the chest, or letting them hang down. The hadith of Wāʾil ibn Ḥujr is used as evidence for placing the right hand over the left on the chest, but Ash-Shawkani objected that while the Shafi'is advocate placement under the chest, the hadith mentions "on the chest." However, some Shafi'is mentioned a narration with the wording "under his chest" to clarify the meaning.

As for celebrating the Prophet's Birthday (Mawlid), it is an innovated bid'ah.