Well, obviously, you need to have Qt compiled with MSVC2012 compiler to compile projects with it. Or get MSVC2012...
You should also know that VS2012 compilation is likely to produce wrongly named lib files, putting an extra 5 after the name of each file, renaming the files to remove the trailing 5 fixes that.
As for the headers, there has been some rearranging, make sure the include folder of Qt5 is into the project properties - C++ - general - additional include directories, the add on should add those, but if not, you should add manually. Id you still get an error trying to locate some headers, go and search for them in the include folder to see if they aren't moved to some sub-folder.