So far as I know, a committee must have specific councillors appointed as its members. All of the members should receive a summons for a meeting, and the same rules about publishing the agenda three clear days in advance apply to committees as to the council itself. Committees are automatically dissolved each time the annual meeting comes round in May, and need to be reappointed. This is a convenient time to change either the nature of the committees or their membership.
The legislation does not require the agendas to be sent to the full council, although I would think it good practice to do so. One action you could consider would be proposing that sending committee agendas to all council members should be made obligatory through a change to standing orders or an instruction to the clerk. The council of which I'm a member sends agendas automatically to all councillors and also allows members of the public to add themselves to the mailing list; agendas are accompanied by all relevant supporting documents.
It is widely accepted good practice for every meeting of the council or its committees to allow time for members of the public (or councillors who are not committee members) to speak to the committee. Again, this could be added to standing orders or be an instruction from the council to the clerk. Quite a few councils now permit members of the public to speak at the time an item of interest is discussed, although the chairman must always have the authority to control the meeting.