No she is not Rock Hudson's daughter. In fact, they are not even related. Kate Hudson is the daughter of Bill Hudson and Goldie Hawn. But she was primarily raised by Goldie Hawn and her boyfriend, Kurt Russell.
Yes, her daughter is Kate Hudson. Kate is the daughter from Goldie's marriage prior to her partner now of many years Kurt Russell, last I knew they have yet to marry but are very committed to one...
No, she is the daughter of actress Goldie Hawn and Bill Hudson,who is himself an actor, comedian, and musician. However, she was raised by Goldie and her boyfriend Kurt Russell.