1) based on my testing, it does have to run under the admin account or a user in the admin role. based on your question, i created another splunk question to get help: http://splunk-base.splunk.com/answers/75013/minimum-permissions-required-for-using-http-simple-receiver
2) seems to be the case. although, to be clear, this is not necessarily tied to the FireEye app but to anything that attempts to use the http simple receiver, REST endpoint.
3) you don't need anything in inputs.conf. the http post specifies the input and the neccesary parameters.
4) in your scenario, fireeye is sending the data to the forwarder. so the user/passwd you use in the fireeye config must have the appropriate permissions in the forwarder.
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