Iis – Configure IIS for Exchange Management Console

I'am newbie to IIS and Exchange Server, and I did not know that Exchange Management Console and Exchange Management Shell use IIS, so I removed IIS from my mail server. Now we get emails and we can send emails, but we can not start the Exchange Management Console or Exchange Management Shell to add or edit users and so on.

I get the following error message when I try to start it:

(Click to enlarge)

I have searched the internet, and what is clear is that IIS is necessary for Exchange Management Console or Exchange Management Shell to work. And there is a problem with Kerberos authentication.

So I re-installed IIS but things still not work, so the default config is not enough.

I have searched for the solution in last 3 days and have tried out some promising solutions but have not succeeded. I'm new to this things so I dare not do everything what I read, because it could break the things down more heavily.

So I really appreciate if someone could write down to me how I should configure the default site or one new site in IIS to work properly with Exchange Management Console and Exchange Management Shell step from step.

Additional info: Server run on Windows Server 2008 R2 and Exchange version is 2010 and IIS version is 7.5

UPDATE: Due to the character restriction of comments I reply here:

I got always the same error in Server Management when I try to add bindings to the default site (any protocol) The error message: The World Wide Web Publishing Service (WWW Service) did not register the URL prefix %1 for site %2. The site has been disabled. The data field contains the error number.

The support page of this error: http://technet.microsoft.com/en-us/library/30eb8114-5a0d-4bd7-bd99-fa5a8df7e3ca.aspx

And I fount in the Events the detailed error of the problem. ( They comes since I uninstalled IIS)

An unexpected failure has occurred. The problem will require administrator intervention. The service will retry in 15 minutes. Diagnostic information:
a következő helyen: ( "a következő helyen" in english looks like: at the this place) Microsoft.Exchange.Management.Metabase.IisUtility.CreateIISDirectoryEntry(String iisDirectoryEntryPath, TaskErrorLoggingReThrowDelegate writeError, Object identity, Boolean reThrow)
a következő helyen: ( "a következő helyen" in english looks like: at the this place) Microsoft.Exchange.Management.Metabase.IisUtility.FindWebObject(String parent, String name, String type)
a következő helyen: ( "a következő helyen" in english looks like: at the this place) Microsoft.Exchange.Management.Metabase.IisUtility.FindWebDirObject(String parent, String name)
a következő helyen: Microsoft.Exchange.Servicelets.RPCHTTP.Servicelet.FindIISVDir()
a következő helyen: Microsoft.Exchange.Servicelets.RPCHTTP.Servicelet.Work()
An error occurred while trying to access the IIS metabase. Make sure that the IIS Manager is installed and configured correctly.

So this look like the the root of the problem, but I still don't know how to resolve it.
I read that IIS Virtual Directories recreation is needed but I don't know how to do it.