Hi Daniel
Few outside users in our landscape gets error for searching knowledge articles on HTTPS connection
For this error kindly refer the SAP Note
1762517 - Knowledge Article Search on User Status
1663750 - Knowledge Article Search with TREX and/or Report Framework
1591617 - Authorisation error message during knowledge article search
1)where their erros will be logged at TREX system
2)general erros log files of TREX system
Trace and Log Files - Search and Classification (TREX) Security Guide - SAP Library
3)How to find the connected portal system with TREX..I am not sure about the connected portal system with TREX in the landscape
TREX Admin Tool in the SAP System (TREXADMIN) - Search - SAP Library
Regards
Ram