I am a student and wanted to do some research on graphene on how to mass produce it and I was wondering before starting my project on the wondrous material. So my question is, Is this a free patent? Am I allowed to test graphene?
Nobody can stop you from playing with Graphene-- it is in your pencil. Graphene wasn't invented, it was discovered.
Means of producing graphene (such as in sheets) and ways to use it are being patented.
So you can do experiments on it and ways to produce it. If you want to develop and commercialize your own way to produce or use it, then you need to consider a strategy for dealing with the IP. I won't advise you on those legal issues, but here is one nice reference: http://www.neustel.com/Patent-Infringement/How-To-Avoid-Patent-Infringement.aspx
Further to this, experimental use of patented inventions does not generally constitute infringement under the doctrine of experimental use. It is part of the quid pro quo bargain of patent systems.