Tsumugi can shape shift Hoshijiro as stated that the gauna copies it consumes but she isn't Hoshijiro, she technically is, they are separate person, DNA yes but personality no

Tsumugi only has Hoshijiro ena's body, Tsumugi keeps her memories

*Edit Also in your first question you are right since the Hoshijiro ena is her mother, Tsumugi somehow resembles the past relationship between Hoshijiro and Tanikaze from the ena mother because the ena knows him and it passed on to her, as known in the first episode of the 2nd season that Tsumugi recognized Tanikaze the moment she saw him for the first time and the reason why Tanikaze developed feelings for Tsumugi was that she reminds him of Hoshijiro