Something is terribly wrong here. Either the someone had lied to you or had no idea what he was talking about or you got it wrong.
1)You don't have to submit criminal records for OINP - at least for the Human Capital Priorities Stream and the French Speaking Skilled worker stream.
2) I believe you are talking about the e-APR (the online application that is submitted after an ITA is issued).
3) If your application is rejected, you cannot access your online application anymore. You can either raise a CSE and re-open the application (if you believe you have been rejected in error) or you can submit a fresh application after rectifying the error with your previous application.
4) Once you submit a new application, the application will follow the same path - I am not aware of any special path available for applications that are submitted after the first application is rejected. However, there is a theory that when an application gets rejected and a second application is lodged soon after, it gets processed faster. "Asivad Anac"'s application is one example.