The agent log states that the remote server is localhost so it attempts to connect to the ESET PROTECT server on the same machine. Try re-installing the agent and specify a correct IP address of the server.
Could you please check ESMC/EP trace log for possible hints? Can you verify that service "eraserver" or process ERAServer are actually running? After update, there might be some time during which console is not able to connects - during this phase, database migration is performed, but it should not take very long in case you do not have huge database size/content.
Also you have updated ESMC to EP in existing appliance, or upgrade using "appliance migration" was used? If first is the case, how old was original appliance? If it was much older, there might be possibly issues with dependencies.
Policy > actions > new > settings > user Interface > star mode > Silent > Assign target client > check > finish.
Silent: No notifications or alerts will be displayed. Graphical user interface can only be started by the Administrator.
The error means that the http response 405 Method not allowed was received.
Do you connect directly to the Internet or through a proxy server or firewall? Could you try connecting trough a different ISP?
No. The license will be valid for 1 or 2 years, depending on what license you purchase and will enable you to install ESET on 3 devices. We do not sell licenses for 3 years and 2 years are maximum to my best knowledge.