I'm not quite sure what you're trying to do because your post talks about both designing/running workflows and instance details as well as different activities, but I'll go through it in order and try to clear out the confusion about connections between various parts.
Workflow activities that connect to Laserfiche use the Laserfiche connection profile specified for the workflow definition. This uses LFSO (in versions before 9.1) or Laserfiche.RepositoryAccess to connect to the Laserfiche Server. No ODBC drivers are involed, no Windows authentication is supported. This connection profile is used while designing workflows and, on the Workflow Server, when running workflows.
Data activities (Query Data, Insert Data, Update Data, Custom Query) connect to 3rd party data sources using ODBC or OLE drivers. The driver type and connection information is specified in the data source setup. If Windows Authentication is specified, then the connection is made using the service user for the Workflow Server service. This has nothing to do with the authentication information on the Entries tab in the instance details.
When looking at the instance details, on the Entries tab, we require the user to log in. This was done for security purposes as some users may be allowed to see how the workflow went, but not where the document currently is. The user can specify a LF user or Windows Authentication (no ODBC is involved). The user can specify the same information as the connection profile, but they are not expected to. This information is not saved and, as mentioned above, this connection to LF will time out and disconnect itself if not used for a bit. In your case, since you're also designing workflows, you already know the password for the connection profile, so that's probably why it feels somewhat weird to be asked for authentication again. The feature was designed with users who may have less rights to WF/LF in mind too. This connection defaults to Windows Authentication since that is the more common way of logging into Laserfiche as a regular user. Being prompted for authentication in the Entries tab in the instance details is the expected behavior and not an indication of any connection issues between WF and Laserfiche or between WF and 3rd party data sources.
"Connection to the Workflow Server 'localhost' could not be created." means the WFServer cannot be contacted. If you're seeing this on the Designer on the WFServer, it usually means that the WFServer is not running.