Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
No doubt that the book "Fazail-al-Amal" contains matters which contradict to Qur'an and Hadith. It is not permissible for those people to rely on it. The facts you mentioned in your question are innovations and deviations. The gravest matter is you mentioned that some pious people "are able to know what is going on in the minds or hearts of people". Believing so or claming it is a big sin it can even be considered Kufr if it is proven that the person believes or claims it. Only Allah knows the unseen. Praying behind any person who believes in such things is not permissible. The same rule applies to the one who supports these deviations or defends them.
Imam Ahmad said: 'Do not pray behind any one who preaches his innovations'. Imam Ibn Qudamah said: 'The saying of Imam Ahmad proves that everyone who prays, behind the one who publicly practices his innovation, preaches it or defends it should repeat his prayer. If the one believing in innovation does not show it to people then the prayers performed behind him do not need to be repeated. There is no excuse for the one who prays behind an innovator who shows his innovations to people. So, one who prays behind him should repeat his prayer whereas the innovator who hides his innovations from people the prayer performed behind him does not require to be performed again'. [al-Mughni 2/21]
Friday and feasts prayer should be performed behind any Muslim regardless of his being pious or not. Imam Ibn Qudamah said: 'Imam Ahmad and the scholars in his period used to pray those prayers behind al-Mutazilah (A group of innovators)'.
So, you should look for another mosque which is not dominated by innovators and whose Imam is not a follower of innovations. If there is no such mosque then join other followers of Sunnah and appoint an Imam who avoids innovations. If it is not possible then try to specify a place where all of you can perform prayers. We warn all of you of anything that could cause discord among Muslims. You should always keep in mind the benefits of the Sharia and that Sharia forbids anything that causes more harms than benefits.
If you suspect any discord among Muslim then pray in your house alone till Allah provides you with a mosque, which is free from innovations.
Allah knows best.