Travelling while applying for UK citizenship

I'll be applying for UK citizenship in August and DH and I are trying to work out holiday plans for the rest of 2015.

I'll be applying through the document checking service so I think I'll be able to hold on to my US passport.

Can I use my US passport + ILR BRP to travel between applying and when my application is decided? I know I'll need to be in the UK to do biometrics. They seem to be sending out the biometrics invitations quite quickly so that shouldn't be a problem.

If we have a holiday booked and my application is approved before we set off, am I still ok to travel if I haven't done the citizenship ceremony yet?

I know I'm not able to travel on my US passport + ILR BRP after I've gone through with the citizenship ceremony so I don't plan on doing that.

I know I'm not able to travel on my US passport + ILR BRP after I've gone through with the citizenship ceremony so I don't plan on doing that.

I am also about to apply for citizenship (can't believe I've been here almost 6 years) and am curious about the period between the ceremony and receiving a UK passport. Somebody told me that you can use a US passport with the naturalisation certificate to re-enter the country, Is that true?