Good paper.
I don't think so. If you will use some poor random number generator, the whole thing will probably collapse. Also, if you use some constants as random numbers, it will work like any other function and it will be fully deterministic.
As NotATether said, the "randomness" of parameters should be called "arbitrary".
The whole problem of this paper is that it just made an assumption that generating truly random numbers is trivial. It is not, it was showed many times in practice that many random number generators are poor. And if you take randomness out of this scheme, this is just another function, maybe more complex than existing ones, but that's all about it.
If your construction is correct, this will be a great discovery.
Because of putting too much trust into random numbers being random, I doubt it truly proves that P!=NP.