I have tried to look over the web but there are contradicting statements. Some of the posts from online forums say this is not being supported.
Can anyone please confirm if ACS supports the scenario where the replying party application (and optionally the STS) is hosted in Azure cloud as a Webrole. If the answer is yes, does one need to do some extra changes in the application and config setting for making it happen?
I have tried to attempt it by deploying a sample application and configuring the ACS to get it authenticated through Windows Live ID. It does not get to the STS and fails with the error "Server Error in '/' Application." which means some address is not being resolved or reached.
Does someone have any idea?
Yes, this is a supported scenario. Look here for samples: http://claimsid.codeplex.com
The only special consideration for Windows Azure deployed apps relying on an STS (like ACS) is that the you will need to change the default cookie encryption mechanism for one that is "web farm friendly". This is very well documented in the samples above and supported by WIF out of the box.
Hosting your own STS on Windows Azure is also possible. You would typically deploy it on a Web Role. Howeverm it is not 100% clear to me why you need it from the description above.