What is the ruling on not praying Friday prayer and instead praying Dhuhr prayer in its place continuously for nine consecutive months due to the absence of another mosque free from innovations, and due to security investigations of mosques?

The fact that the congregation or the Imam of a mosque are innovators (Ahl al-Bid'ah) does not prevent one from praying with them, as long as their innovation has not reached the level of major disbelief (kufr akbar) and one cannot find another mosque. As for amulets made from the Qur'an, there is a difference of opinion regarding them, and the majority view is that they are forbidden. However, this prohibition does not lead the one who uses them to disbelief or innovation. It is not permissible to miss Jumu'ah prayer merely because of an summons for interrogation, but if you fear harm to yourself, then it is permissible to miss it. You must not abandon Jumu'ah prayer unless the Imam's innovation has reached the level of disbelief, and you cannot find another Jumu'ah prayer, or you fear harm to yourself. In these cases, you pray Dhuhr.