Do I or my children born in 2005 and 2007 have to apply first for EEA PR before they can register as British?

[kansasstlouis]

Hello,

I am trying to understand how my children can become British citizen. My wife and I are German and we came to the UK in 2000 and have lived here every since and have two children born 2005 and 2007.

My understanding of the citizenship status of our children is as follows
Our daughter is born British because she was born after 30 April 2006 and her parents, have acquired permanent residency in the UK prior to her birth because we have resided in the UK exercising Treaty rights for more than 5 continuous years (albeit not documented), since we were/are economically active in the UK as a worker.
Our son is entitled for registration of British citizenship because he was born between 2000 and 2006.

My question is which applications do we have to do to get to their British citizenship? Do we all (parents and both children) first apply for EEA PRs (with evidence of our residence from 2000) and then my daughter applies for a British passport like any other British national and my son applies to register as British either via 1(3) or 1(4) and if so which one?

1(3) - “A child born in the UK whose parents are not British citizens and were not settled in the UK will have an entitlement to register when one of their parents become settled in the UK or become British citizens” - Guide MN1 page 8
1(4) - “If a child lives in the United Kingdom for the first 10 years of their life, an application can be made

Or is there a more direct route? And if so is this as likely to get approved? Also it will be very difficult to identify all the days we left the UK over the last 18 years. Will this be required in any step of the process?

Any advice would be greatly appreciated.

Many thanks

[Obie]

Were the 2 children born in the UK?