Q: What is the black and red icon (dollar sign with a line through it) next to the active problem I have just added?

From Galen Healthcare Solutions - Allscripts Enterprise EHR Wiki

A diagnosis preceded by a dollar sign with a line through it indicates the diagnosis is not billable and requires an additional digit, to be submitted for billing. The organization indicates how non-billable diagnosis are utilized in TWAdmin/Charge Administration/Enterprise Preferences. If allowed by the preference in TWAdmin and the user selects a non-billable diagnosis, the system creates a Manage Charge Edits task.