I saw Piranha 3D
. I should probably be embarrassed to say that, but the whole movie was just so shamelessly, gleefully lowbrow that you couldn't help but enjoy it.
The severed-penis gag was an especially nice touch, and one of the few really effective uses of 3-D in the film.
Sounds like they're making the sequel in the same spirit.
To answer the OP's question: I'm pretty sure the new film is unrelated to the first two, though I haven't actually seen Piranha II: The Spawning