As stated the council are invited by the planning dept to offer their observations on planning applications. Their remarks carry no more weight than any other member of the public but they could be placed, from a historical point, in a position to bring to light planning matters that may be over-looked or relevant.
Your chair has no other powers than any other councillor other than to chair council meetings and if requested by council to represent the council outside the chamber. To do so they would require council to grant that power and specify it.
It is impossible to invite "ones self" anywhere as one can only be invited by a third party. You can impose yourself but if course a councillor wouldn't do that would they?
As far as I know plans remain the copyright of those who produce them ( architects etc) and cannot be reproduced or printed without express permission. I assume planning departments have permission to display them online.