Audit firm structure?

Hi all,
I am trying to understand the different roles of an audit firm and who has influence over the audit opinion.

Kaplan Fixed Test 1.
What is a manager in an audit firm?
Does the manager run the audit, gather the evidence and work with the client?

What is an engagement partner?
Does the manager report to the engagement partner and then the engagement partner deals with the client?

What is an audit senior?
Finally does the engagement partner submits the report to the audit senior for review and signature? If this is the case then which ones need rotating?

By understanding who does what it influences what ethical threats exist between auditor and client, I hope.