If the child is born in Poland it will have the mothers nationality.
Yes, but if the child is born outside Poland, it will also have Polish nationality.
To register the child for a British Passport you need to submit all details to the British Consulate, at least 30 days prior to the birth.
That is correct, to a point
InKrakow is correct, you have to be married
Not anymore. The Home Office Border and Immigration website (says "If you were born in the United Kingdom on or after 1 January 1983, you are a British citizen if at the time of your birth one of your parents was: a British citizen; or legally settled in the United Kingdom."
There is also
which says "Section 3(1) - illegitimate children of British citizen fathers Until 1 July 2006 a child could not acquire British citizenship through his or her father if the parents were not married at the time of the birth. If the parents married after the birth, the child may now be considered legitimate."