The amarr legal system ist very complicated and I don't think it is only because of the lack of PF
but also because it appears to have developped rather than having been designed.
Imagine the state of the english judicial system of the 12th century with a strong papal influence.
Local feudal holders hold court creating very diverse law all through the empire. When things get out of hand, imperial authorities intervene,
creating a common imperial law on a case by case basis. We don't know when the Civic Court was formend and what exactly it's jurisdiction is but we know that the Theology Council, which I expect to be the older of the two, was formed after the Moral Reforms during a period of increased centralisation and has now (almost) exclusive jurisdiction in religious matters only to be overturned by the Emperor or Speaker of Truth. Also we should expect the Council to not just hear anyone but be reserved for holders or complaints against them.
So in practice it should be like this:
Usual way:
Any case arises
Take it to your superior holder when he holds court.
Have a problem with his judgement?
I Are you a joe-amarr commoner? ->to bad
II If you are a holder or for some other reason of import:
a) Did the Holder err in a religious question? - Appeal to the Council (Speakers are used so rarely and are so powerful that we should probably stay away from them)
b) The Holder violated Imperial law? -> Appeal to an imperial authority if one exists with jurisdiction over the specific case.
Local holders will hear any case, even those which fall under the jurisdiction of an imperial authority.
This authority will only get involved if they deem a matter important enough or are called upon by a holder, either one seeking judgement ore one referring a case he does not wish do decide.
This idea of a highly regionally diverse legal environment with a central authority exclusive to higher classes and in cases of general interest is perfect for rp as there is a lot you can do with it. Who said, it isn't the law on that obscure planet somewhere in the mandate that a yearly lottery is held to show god's will as to who has to marry whom and that occasionally this accidentally lead to incestuous or homosexual matches?
The only thing we can't really do is make up the binding imperial law. All we can do here is interpret prime fiction.
As to judicial duels, meaning duels meant to create a legally binding outcome:
They are possible as a judgement themselves,
Judge Superholder thinks god should decide the outcome of the case and has the two underholder adversaries duke it out.
a means agreed upon by both parties to resolve the conflict,
or a menas requested by one party and agreed to by the judge to either settle the wholfe conflict or decide the facts of the case if they are contested.
A "right to trial by combat" is more complicated.
The ancient tradition might still exist locally but on an imperial level it would, after the development of the common imperial law, be an extremely rare and limited relic.
They are, if at all only thinkable between equals and not in cases over which an imperial authority has exclusive jursidiction, such as
the Council over religious questions. Otherwise a strong duellist could even contradict the emperor's words spoken with the voice of god.
In the end, if the vast majority of the rp community says: there is or there is no general right to trial by combat, then this is what it wil be until PF contradricts us. This is our only means of protection against RP trolls but should be used with caution as excessive use of majority priviledge may interfere with people's different but legitimate views. Special restraint should be shown in using IC authority to influence lore the environment for others.