1- Yes according to Islamic Law it is permissible for a Sayed female to marry a non-Sayed male. However, he must be religious and have good Akhlaaq.
2- Inter sect marriages are allowed, provided that the spouse who is on the path of Ahlulbayt (a) guarantees that he/she will stay firm on their Shia school of thought and not be pressured to give up some of his/her faith. Some spouses get married and then over time they end up with a weakened faith. One cannot put himself/herself in this situation.
It is generally not encouraged because usually it leads to tension when it comes to raising children and deciding other religious matters. The Sunni parent wants his children to grow up to be Sunnis. The Shia parents wants them to be Shia. The in-laws usually get involved and put pressure. This leads to tension and difficulties, and it’s not wise for someone to put himself/herself in this position.
3- If her father is justified (meaning there is a good Shia suitor but she wants someone who is not Shia), then she needs his permission to get married. It he disapproves then he is justified, but he has a right to ensure that his daughter marries one who has complete faith. Yes, he cannot force her to marry a specific person. It has to be with her consent.