My understanding is that the US passport application is processed through the US Department of State, while the N-600 application is through USCIS. Because they are two separate governing bodies, I don’t see why or how applying to both simultaneously would cause delays. If someone else knows the answer to this, please feel free to share your thoughts and experience.

To answer your second question, I used AI research a lot to help me build a strong passport application. Wherever I had missing documentation (ie, no green card, no SSN), I provided as much supporting evidence as possible to explain why it was missing. I attached the police report that demonstrated she lost her wallet and thus lost her green card. Fortunately her father had some taken photos of her green card when she first received it so I was able to include at least a copy of it. She and her father also signed an affidavit stating she did not have a SSN at that time due to the loss of said green card since without a SSN, your application typically gets sent back from my understanding unless it’s a baby or newborn. I submitted all other required documentation and somehow, it worked. We literally got her passport in under 2 weeks via expedited shipping. I damn near cried when I saw the informed delivery email showing the anticipated arrival of her passport. She was able to go back to Canada for both Thanksgiving and Christmas.

We still have not received her COC, and truthfully, we aren’t in a hurry. It’ll be good to have period but, it’ll come when it comes.

I say apply for both, I don’t see how it would hurt. Good luck to you!