Is it permissible for a group to control the mosque, set prayer times, and delay them according to their circumstances without consulting the rest of the community members?

Mosques are for the general public, and no one has the right to control them by setting prayer times that suit only them without considering the congregation. The determination of the time is referred to the regular congregants of the mosque; if they agree upon it, they act accordingly. If they differ, the decision rests with the authority responsible for the mosque.