Traveling out of UK between cit. app and biometrics appointment?

I'm trying to decide on the timing of our citizenship applications.  We are eligible on 9 September, however I have a trip to Ireland planned at the beginning of October. If we send in our application, but I can't get a biometric appointment until after Ireland, is that OK?

Another question: My US passport expires next April.  If I do the British citizenship application but renew my US passport before getting a decision from UKVI, do I need to scan and upload the new US passport to them?

You can travel during a naturalisation application, as it's different to a visa application.  You'll hold onto both your passport and BRP during the application process.

Honestly, I have no idea about the renewed passport.