Canon law has nothing to do with civil law.
Neither does sharia, in this country.
This is very simple. Ahmed and Abdul have a business dispute. This “court” would allow them to take their dispute before the “judges” who would rule on the case according to sharia.
The court would have no way whatsoever to enforce its rulings other than public opinion in the Muslim community, and it would have zero force of law in this country.
It is roughly the same as if a group of Trekkies agreed to settle their disputes using Klingon law. Any party who did not want to would just refuse to accept the ruling. End of story.
Canon law professionals provide mediation and arbitration services. Not very different from what this court would provide, in practice if not in theory.
http://www.canonlawprofessionals.com/mediation.html
Not even close. The maximum penalty a Catholic canon law court can impose is excommunication from the faith. I'm fine with that and wish they would use it more often, especially with the pro-abortion politicians who use "their Catholic faith" as a fig leaf to counter what the church teaches.