1. Dear *****tian, you don't automatically get a British passport upon marrying a British citizen. Instead, you need to live in the UK for five years continuous residence and then you will get British citizenship and a passport. Secondly, your daughter will get UK citizenship by descent because one of her parents is a British citizen. However, it is essential that you register the birth and take out UK citizenship for her before she reaches 18 years of age.
2. Your daughter can hold dual british and Polish citizenship. The process of applying for UK citizenship is no different if she already holds Polish citizenship. If your child was born outside the UK she fills in Form MN1 at this link https://www.gov.uk/government/publications/application-to-register-child-under-18-as-british-citizen-form-mn1
If your child was born in the uK there is no need to register.
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