I build applications using VS2013 and PhysX-3.3.2 or PhysX-3.3.1. There is no problem using the PhysX libraries with VS2013. Please post more details about the problem you encountered with VS2013.
Regarding CRT, please see the following note in the User Guide. I don’t think anything changed here from 3.3.1 to 3.3.2, so I don’t know why you would suddenly encounter problems that didn’t exist in 3.3.1. If you have more specific details, please post them.
At a minimum, applications need to link against the following libraries with the appropriate platform extension (e.g. “.lib” or “.a”) and with * being a x86 or x64 for Windows platforms:
The static libraries we provide with the Windows binary distribution are linked against the Multi-Threaded static C Run-Time (CRT) libraries. This means that your application must also use the same CRT flavor. If you need to use a different CRT version, you must upgrade to our source license. The source distribution can simply be recompiled using different CRT settings.
For PhysX3Extensions, PhysX3Character, PhysX3Vehicle, etc., you can rebuild the libraries using the solution found in \PhysX-3.3.2_WINDOWS_SDK_Core\Source\compiler.