Episode 3

[GonzoStyle]

Because Leia is adopted by senator Organa and she grows up with no knowlege of padme as her mother, as far as she is concerned she is Princess Leah Organa. Bail Organa is a member of the royal house of alderaan and is royalty as are his children so thats why she is princess leia. She also eventually becomes the youngest elected senator of the galactic empire before its dismantled and then she joins the rebel alliance of which her father (adopted father) is a major player in.

Thats why in episode 4 she sends the message inside R2 to find obi-wan so he would go to alderaan to meet "her father" but the death star destroys the planet of alderaan before he can make it.

As far as the droids, after the scene where luke and leia are broken up senator organa offers to take in leia, once he leaves the room he orders that the droids memories be erased and thats why they have no memory when they meet luke or come back to the skywalker home where young anakin grew up and where 3po was built and where luke lived. though you'd figure lukes uncle would.