Is this informal church “tribunal” authoritative under ecclesiastical law?
There is no such thing as an “informal church tribunal”. It’s very formal and is operated by the Diocese under the authority of Rome. They appoint Dioscesan attorneys to represent the plaintiff. If the defendent wants an attorney, I’m sure they would appoint one for the defendent too. Of course, that increases the cost.
The only time the decision goes to Rome is when there is a dispute, and one of the parties does not want the annulment. Then the decision can be appealed to Rome, whether the Tribunal decided yes, or no.
The Diocesan marriage tribunal uses lay people to decide the case. There are psychologists involved and attorneys and transcriptionists and notaries. Lots of paper work. It’s a big deal.
You wrote:
“Is this informal church “tribunal” authoritative under ecclesiastical law?”
Not even remotely. It would be like if five or six of your buddies got together and said, “Oh, So-and-So’s marriage is not a true marriage.” It’s utter nonsense. Now, to be fair, they may be absolutely right in their conclusion (I have no idea about the circumstances surrounding Mel’s marriage), but it is ridiculous for these lay people to think they can be wield the authority of an official Church body when they are in practice not even part of the Church.