If you mean by "engine running or not", that it runs with the key off, then the installation was done incorrectly or a relay failed catastrophically. If you mean it starts running with the key on, but the engine not running... that's expected. As for the return line... what did they do with the OFV connection on the back of the p-pump? An electric pump that can modulate it's own pressure to keep the IP at 30-ish PSI doesn't really need a return line, I guess? Did they just cap everything off? What'd they do with the return line from the injectors?
Honestly, OP... ^^^ this. Almost nobody needs an airdog/FASS on a 12V, and they tend to get thrown on as a very expensive bandaid instead of properly diagnosing/fixing a fueling problem, or somebody 'heard it was good' without actually understanding why -- they are a significantly better upgrade on some of the newer trucks, but not ours. The stock LP and fueling setup is far more reliable/long-lasting than any electric pump and moves more than enough fuel to support 550-600 HP.Sell it and go back to oem.