First British (Adult) Passport Illegal Immigrant/Overstayer Mother.

[NoAnswer]

Hi Everybody. I've been looking at these boards for a long time. My questions are regarding a first British (Adult) Passport. Can children of an illegal immigrant/Overstayer Mother apply for a passport?
The parents are married, so would be getting their BC through their British born father, correct?? When the kids apply for a passport will this cause problems for the illegal mum with the Home Office at any point? What about the interview stage? (The children still live at home). What documents have to be sent off? Kids full Birth Certificates, parent's marriage certificate, and father's passport number? (Obviously mum doesn't have one). Will HMPO request any documents relating to the mum? Kind regards. Thanks in advance for your answers to my questions.

[wahi66]

you post is very difficult to understand the situation.
are you the father?
could you please state the full detail including the mother's full immigration history, children born year etc.