I'm hoping the letter comes quickly enough so I can get the ceremony portion of the process done by the end of the year. Then I'll just have to do my passport after the new year and be good to go 🤞
There is no rush to naturalise as a British Citizen, although the fees go up. A valid ILR allows you to remain in the UK and travel in and out of the UK, as long as you don't remain outside the UK for more than 2 years. ILR is the end of the immigration route. Some migrants never apply for British Citizenship.
As stated above, you must return your BRP within 5 days of your ceremony (where you received your Certificate of British Citizenship).
https://www.gov.uk/apply-citizenship-spouse/after-you-get-your-certificateA British Citizen must not have a visa to the UK, or be granted a visa to visit at the border. If you can get to the UK border, you can go to an immigration officer with your proof of British Citizenship, but expect a wait while they check the records.
You won't have your BRP to show an airline as that in no longer valid and you would have returned it. Keep an eye on which date next year US citizens are required to have an ETA to show an airline. Following Brexit, the UK had brought in new laws to also carry out what Australia and the US have already done.
https://www.gov.uk/government/news/uk-unveils-plans-for-travel-scheme-to-bolster-the-borderBritish Citizens can't have an ETA. British Citizens have a right to enter the UK.