Is it permissible for the Imam to combine the Asr and Jumu'ah prayers every week without a valid excuse, knowing that discord has spread throughout the mosque and that the Imam has been combining the prayers for the local residents and others for two years?

It is not permissible for the Imam or anyone else to combine two prayers without a valid excuse. Therefore, if someone combines them as jama' taqdim (combining the later prayer with the earlier one) without a valid excuse, their second prayer is invalid because its time has not yet entered. And if someone combines them as jama' ta'khir (combining the earlier prayer with the later one) without a valid excuse, they have committed a sin by delaying the first prayer beyond its prescribed time. Causing discord is absolutely impermissible, especially in the mosque, just as raising one's voice in the mosque is prohibited except out of necessity, such as reciting aloud during prayer or delivering a sermon.