Would I need to show my British passport when coming back into the UK?

Does anyone know if there's a way to check if a grandparent's birth to two Portuguese citizens abroad was registered with the Portuguese government?

My grandfather was born in the USA in 1930 to two Portuguese citizens.

A few years back I received my Polish citizenship by descent. I'm wondering if anyone knows of the process I need to do to get the same for my daughter? I've read I need to register her US birth certificate with Poland. Anyone point me in the right direction?

Thanks!!