The rules do not give any guidance on important non-procedural
elements: the standard of proof (is it akin to civil? criminal?),
determination of relevant law, what cases can be cited, admissibility
of evidence, etc. Where can I find answers to these questions?
Generally, arbitrators apply the substantive law of the jurisdiction applicable to the dispute, and the procedural rules of the arbitration forum, and their own views when neither applies.
But this is not a legally enforceable obligation of an arbitrator. An arbitrator can grossly disregard the law and need not follow any rules of evidence other than to allow you to present all relevant evidence. If the arbitrator wants to apply the Pirate Code of a Hollywood Film, the arbitrator is within his or her authority to do so and will not be reversed for doing so when the prevailing party seeks to have the award confirmed.
Also, while you can seek to set aside an arbitration for particularized bias in a given case, you generally cannot do so out of systemic bias in favor of the party drafting the arbitration clause, even though that is well established empirically.