Yes, they discover that in episode VI, Return of the Jedi
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The spirit of Ben Kenobi revealed to Luke he had a sister and Luke sensed it was Leia
Yes. They didn't find out until they were 23 years of age because they were separated at birth
Yes. You find out in Return of the Jedi (VI).
Since Leia and Luke are twins, they are the same age. They were born 19 years before A New Hope happened. Both Luke and Leia are 23 years old in Return of the Jedi
Jacen, Leia's son, killed him in a lightsaber duel.
Luke Skywalker was actually born on Polis Massa as his mother and Obi Wan were fleeing the Empire. After Luke's mother died in Childbirth, Obi Wan split the twins, Luke and Leia, to insure their survival. Luke was sent to Anakin's step-brother on Tatooine and Leia was taken to Bail Organa on Alderaan. That is where they grew up until they joined in the Rebellion against the empire.
A space station known as The Death Star