Can a "Non-Party" of an Arbitration Process get equal Privileges and Rights like a "Party" as per the laws of the United States and its Constitution, when the Arbitrator in fact barred the "Non-Party" to participate in the Arbitration proceedings any further?

Can my agreement of Personal Guaranty be defied, and a Judgement be imposed on a non-party, without any fair trial as per the terms agreed in the Personal Guaranty Agreement?

Can a Supplementary Agreement (here it is Personal Guaranty Agreement) be valid in the absence or without the existence of the concerned Principal Agreement (Master Retailer Agreement) on the date the supplementary agreement was signed?

Can a 'Non-Party' of an Arbitration Process get equal Privileges and Rights like a 'Party' as per the laws of the United States and its Constitution, when the Arbitrator in fact barred the 'Non-Party' to participate in the Arbitration proceedings any further?