Is the mosque committee's action of preventing a man from speaking about religion and Sunnah in the mosque correct? And are there manners for speaking and offering advice in mosques?

The actions of the mosque committee cannot be judged right or wrong without knowing the reasons. Those who call to Allah with insight and sound creed should be supported, provided they seek prior permission from the committee. As for those who are deviant in their creed, one must be wary of them and gently but wisely prevent them from corrupting people's beliefs.