I do use proxy for a process workspace running on FME server.

1) Instead of defining FME-wide proxy address, I would like it to be set in HTTP Caller, so different HTTP Callers could use different proxies.

Yes, absolutely, a lot of our enterprise clients use proxies so it's vital that FME handles it smoothly.

I wish it was possible to set the FME Server proxy settings from the admin GUI, and that they could be set to override whatever was defined in workspaces (HTTPCaller, etc). I posted an idea for this here, for those who want to vote: https://knowledge.safe.com/content/idea/33375/fme-server-proxy-settings-in-admin-gui.html

I also wish that the FME Server proxy settings where honoured by all the services, notably the Amazon S3 subscription service, which currently does not support proxies at all.