You should be able to view the image in the browser, if you access it directly, but it should not get downloaded.
Here is the issue:
IDM Logs - #47;iam/im/IdentityEnv/ui7/ui/images/favicon.ico
Webagent Log - /iam/im/ui/images/favicon.ico
favicon.ico is global to IDM Admin application and always displayed from the url - /iam/im/ui/images/favicon.ico regardless of IME name.
It should not have any reference to IDM environment.
It looks like front-ending webserver is appending your environment context root(IdentityEnv/ui7) while reverse proxying it to your back end application server, thats why you are getting 404 from app server log with invalid path.
Please check your webserver proxy/reverse proxy configurations for any invalid mappings.
Regards
Ashok