"When you grow up, you will become very powerful."
"Kiedy dorośniesz, staniesz się bardzo potężny."
The one above is an exact translation, but this one is also possible:
"Kiedy dorośniesz, będziesz miał wielką moc." (When you grow up, you will have great power.)
Here the word "moc" (power) suggests magical powers.
"You come from an ancient family."
"Pochodzisz ze starego rodu."
Thank you all, very much, for your help!
You're welcome :)