I am getting married in secret without the knowledge of my parents. Will I need my father's permission or will my father need to be present during the Nikah?
Virgin girl does need her father's permission for her marriage if her father is a Muslim and does not reject the marriage for un Islamic reasons. Your father does not need to attend your Nikah but he must agree on it if it is your first marriage.
There are certain cases when this condition becomes void like when you need the marriage to save yourself from sinful act, and your father is refusing the marriage for reasons which are invalid in Islam.
Wassalam.