Anastasia: Did she realy survive and was she Anna Anderson 

No, Anastasia did NOT survive the massacre of the Romanov family. They just buried her not with the rest of the family.

And Anna Anderson occurred to be a Polish woman, who was a servant in the palace of the Tsar Nicholas II. So, that's why she could remember many events and facts.

well noone knows anything for sure, thats why there are so many conspiracy theories out there surronding anastasia, one of them being this movie!