1. The game doesn't delete either the Original family or the Sim you're moving out. Depending on how you move them out, you can either choose a house for them or have the game choose a house.
2. Yes you will be able to see the Sim around town and will remember her family.
3. The Sim will keep their relationship ties with the family.
4. Yes, the game should say who is the Aunt, Niece, Nephew, etc.
5. Yes, the Sim will visit and may call the family.
Please note that if you have story progression on the non-played family members may move out of town. If that's the case, they may loose family ties.