Thanks for the info. You don't have to worry about the Server ANSLIC_ADMIN Utility tool. This tool is rarely used nowadays (there are some customization that can be done here but 99% of the time, you don't need to customize it). You can directly launch ANSYS License Management Center GUI and mange the license server in this tool.
The main issue here is that only the ANSYS Licensing Interconnect is shown as running (this is from your ANSYS License Management Center screenshot). Your FlexNet Licensing is actually down. Please click on the 'View Licensing Interconnect Log' , scroll to the bottom and take screenshot and post it here. Also, click on the 'View FlexNet Debug Log' , and see if there is any line that says 'error'