>>angott+(OP)
There's a lot more than just crypto. Its much more common for systems to fail in the supporting code then it is for the crypto to be wrong. So first step is probably learn reverse engineering and verify the crypto is being used correctly.
Certainly not required. A PhD will teach you a lot about methodology but not necessarily the technical details required and involved in secure multi-party or P2P messaging.
>>colord+7c
Unless the build is reproducible it would be smart for a paranoid person to use the published source code only as a comparison with the decompiled app.