For BEx Web scenarios the most important connection type is the HTTP connection (SAP Note 592085). BEx Web is sometimes called in embedded scenarios, like federated portal, CRM UI or NWBC, where a frame of a different application wraps the BEx web report. In order to access these scenarios, all involved URLs need to be enabled on the SAProuter of a particular HTTP Connect connection, which is assigned to a particular system in SAP Service Marketplace.
Other necessary connections type, depending on the scenario are:
R/3 Support Service Connection - to compare report results, debug and run/analyze traces
SAP NI Connection - to connect internal portals in order to test latest corrections. To connect WAD and BEx Query Designer to customer's BW system
WTS (Windows Terminal Server) - just in case HTTP connection is not possible. It slows down and harms the analysis process, but may be a workaround
In case the issue is regarding BI Java configuration, a user with admin permissions for both ABAP and Java side is necessary.
For general reporting issues, a user with RSTT trace authorizations which is the SAME on ABAP and Java is necessary.
To update logon data, follow SAP Note 1773689 - How to add logon credentials securely to an incident - SAP ONE Launchpad (Support Portal)