If you believe councillors are being bullied then report it to your District Council's Monitoring Officer.
However, the case of a badly run meeting, the standing orders should guide the council, and some of the standing orders are quite restrictive. Ask your chairman to follow them - take a copy they should be available on the Parish Council website.
Note, however the risk of doing so, our standing orders, for example, allow each member of the public to ask one question. As Chairman, I typically allow more than that as it allows the member of the public to be heard and get the full element of their question/problem aired and receive a response to which they can follow up - e.g. when they say they don't like my answer and want to put forward an alternative.
Can councillors make decisions without public communication - Yes. Should they do so without communication depends on a) what the item for discussion is b) whether communication did happen, but people weren't interested at the time (planning!) - does everyone read the newsletter / email / website / facebook page of the Parish? - I certainly can't force residents to do so.
Can councillors do things against public opinion - Yes. They are policiticans (as much as many of them don't want to be) and will in the main make decisions that benefit residents, but sometimes they have to make a decision that will upset/annoy people - putting up the precept being a common item.
As I am not sure what you mean by unauthorised consultations/agreements, I can't comment on that.
