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Can I submit an application for express entry while this application is in process? Would I have to declare that I am n longer in a common law relationship ?

The reality is that, as you have said yourself here, you are no longer in your relationship and don't intend to continue with the sponsorship app. Either you or your sponsor needs to immediately withdraw the app. You can't continue on with it just so that you can receive the OWP and then withdraw; lying to obtain any form of immigration status is fraud.

You can do an EE app whenever you want and you would have to declare yourself as single.
 
Yes, I am still waiting on the OWP permit. I would expect it to arrive in the next month or two. We are still technically in a relationship and have a lease together for another 5 months. I am unsure if we can work through this or not.

You and your partner need to confirm if you're still a common-law couple or not.
If you have both decided you're separating and that is the end of it, then you have an obligation to withdraw the PR app asap.
If you are both trying to work through the relationship issues and may continue being a common-law couple going forward, then there is no obligation to cancel the app at this time, until the separation is confirmed.

Typically it's the sponsor that will immediately cancel the PR app upon any separation, since they are the ones liable financially for the applicant for 3 years once they get PR.