I am new to SSRS and Microsoft BI stack, and want to know if SSRS Report server runs on top of IIS or is it a separate entity (server) that runs independent of IIS?
Secondly how to give public access to a report server? Also is it necessary or the Report Viewer embedded in a site (or application) communicates with the report server on user's behalf?
Microsoft severed the IIS dependency for SQL Server Reporting Services (SSRS) in the 2008 version, everything is set up from the Reporting Services Configuration Manager.
With regards to public access to the reports, there may be some security aspects that should be considered before allowing this.
Here is a good article which talks you through the process of granting anonymous access: http://talksql.blogspot.co.uk/2011/12/setting-up-anonymous-access-for.html
In terms of the Report Viewer's role, see this question for further reading: How does Report Viewer communicate with SSRS?