Is it permissible to pray in mosques controlled by Sufis and ignorant people, where innovations are enforced and those who reject them are exposed to danger, and would prayer in them be obligatory and sufficient?

If it is possible to pray in a mosque other than the one mentioned, that would be preferable. However, if that is not possible and the Imam is free from major shirk (polytheism), then praying behind him is valid, and one should not miss Jumu'ah (Friday prayer) and congregational prayers due to his transgressions. As for the matters mentioned, such as differences in prayer, they are subjects of scholarly disagreement and are not described as innovations (bid'ah):

1. Straightening the rows is recommended by the majority of scholars. 2. Placing the hands below or above the navel during Qiyam (standing) is a matter of scholarly disagreement. 3. Pointing with the finger after mentioning Allah and then returning it is permissible. 4. Placing the knees before the hands when prostrating or vice versa is a matter of scholarly disagreement, and the majority of scholars believe in placing the knees first. The same applies to the manner of rising. 5. Performing the regular supererogatory (Sunnah Ratibah) prayers after the prescribed remembrances (adhkar) is better, but there is no sin in performing them before the adhkar. 6. There is no clear evidence for the legitimacy of consistently performing prayers after the first Adhan for Jumu'ah.