We looked at Identity Server and Starter STS seems large to serve a few encrypted claims. So coming to the question
Is a STS required or mandatory to Federate with ADFS 2.0
We opted for Identity Server since ADFS 2.0 does not support other data stores
Is there a option to serve claims through mvc controllers or something using Windows Identity Foundation and SAML 2.0 Protocol
You tagged this with SAML so I presume that's the protocol (rather than WIF).
I assume your application is ASP.NET?
If you want to federate with ADFS, then Yes, you need another flavour of STS.
IdentityServer does not support SAML to applications.
There is a WIF SAML CTP.
If you want a .NET application to speak direct to a STS using SAML, you can use the .NET OpenSSO Fedlet (or the OpenAM one).