VS2013 Community is really VS2013 Professional with different licensing. Any VS2013 Professional addon will also work in VS2013 Community.

I don't know the answer to this question, but my understanding is that you don't need a paid version of Visual Studio

it does. in fact, that is the default recommendation, ie PTVS installed into Community Edition:

https://github.com/Microsoft/PTVS/wiki/PTVS-Installation