New answers tagged prerequisites
The SP 2013 exe installer needs a file named servermanagercmd.exe, which is not present in the windows server 2012 R2 OS. So we need to rename the file servermanager.exe, to servermanagercmd.exe which is located in windows\system32 directory. This is what has solved my problem.
Yes, VS Community 2013 supports creating SharePoint solutions and apps. I am working through some provider hosted app examples in it right now. The templates should be under C#(or VB) -> Office/SharePoint -- if you don't see them you may not have the Office Developer tools installed -- you can find them here: http://aka.ms/OfficeDevToolsForVS2013
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